La catégorie des algèbres quadratiques est munie d’une structure tensorielle. Ceci permet de construire des algèbres de Hopf du type “(semi) groupes quantiques”.
The category of quadratic algebras is endowed with a tensor structure. This allows us to construct a class of Hopf algebras studied recently under the name of quantum (semi) groups.
@article{AIF_1987__37_4_191_0, author = {Manin, Yu. I.}, title = {Some remarks on {Koszul} algebras and quantum groups}, journal = {Annales de l'Institut Fourier}, pages = {191--205}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {37}, number = {4}, year = {1987}, doi = {10.5802/aif.1117}, mrnumber = {89e:16022}, zbl = {0625.58040}, language = {en}, url = {https://www.numdam.org/articles/10.5802/aif.1117/} }
TY - JOUR AU - Manin, Yu. I. TI - Some remarks on Koszul algebras and quantum groups JO - Annales de l'Institut Fourier PY - 1987 SP - 191 EP - 205 VL - 37 IS - 4 PB - Institut Fourier PP - Grenoble UR - https://www.numdam.org/articles/10.5802/aif.1117/ DO - 10.5802/aif.1117 LA - en ID - AIF_1987__37_4_191_0 ER -
Manin, Yu. I. Some remarks on Koszul algebras and quantum groups. Annales de l'Institut Fourier, Tome 37 (1987) no. 4, pp. 191-205. doi : 10.5802/aif.1117. https://www.numdam.org/articles/10.5802/aif.1117/
[1] Quantum groups, Zap. Naučn. sem. LOMI, vol. 155 (1986), 18-49 (in russian). | MR | Zbl
,[2] Koszul resolutions, Trans. AMS, 152-1 (1970), 39-60. | MR | Zbl
,[3] On the subalgebra generated by one-dimensional elements in the Yoneda Ext-algebra, Springer Lecture Notes in Math., vol. 1183 (1986), 291-338. | MR | Zbl
,[4] Hopf algebras and vector-symmetries, Uspekhi Mat. Nauk, 41-5 (1986), 185-186 (in russian). | MR | Zbl
,[5] Tannakian categories, Springer lecture Notes in Math., vol. 900 (1982), 101-228. | MR | Zbl
, ,[6] Mixed categories, Ext-duality and representations, 1986, preprint.
, ,[7] On quadratic commutation relations in the quasiclassic limit, in : Mat. Fizika i Funke. Analiz, Kiev, Naukova Dumka (1986), 25-33 (in russian). | MR | Zbl
,- Self-duality from twisted cohomology, Journal of High Energy Physics, Volume 2025 (2025) no. 3 | DOI:10.1007/jhep03(2025)053
- Bi-Frobenius Algebra Structures on Quantum Complete Intersections, Acta Mathematica Sinica, English Series, Volume 40 (2024) no. 6, p. 1481 | DOI:10.1007/s10114-024-2370-4
- Hopf Algebra (Co)actions on Rational Functions, Algebras and Representation Theory, Volume 27 (2024) no. 6, p. 2187 | DOI:10.1007/s10468-024-10294-6
- The Koszul Complex and a Certain Induced Module for a Quantum group, International Mathematics Research Notices, Volume 2024 (2024) no. 11, p. 9376 | DOI:10.1093/imrn/rnae043
- Quantum representation theory and Manin matrices I: The finite-dimensional case, Transactions of the Moscow Mathematical Society, Volume 83 (2024) no. 0, p. 75 | DOI:10.1090/mosc/340
- Universal Quantum (Semi)groups and Hopf Envelopes, Algebras and Representation Theory, Volume 26 (2023) no. 4, p. 1029 | DOI:10.1007/s10468-022-10122-9
- Koszul Monoids in Quasi-abelian Categories, Applied Categorical Structures, Volume 31 (2023) no. 6 | DOI:10.1007/s10485-023-09756-7
- Generalized Koszul algebra and Koszul duality, Journal of Algebra, Volume 619 (2023), p. 643 | DOI:10.1016/j.jalgebra.2022.12.023
- Quantum Operads, Dialogues Between Physics and Mathematics (2022), p. 113 | DOI:10.1007/978-3-031-17523-7_5
- Veronese and Segre morphisms between non-commutative projective spaces, European Journal of Mathematics, Volume 8 (2022) no. S1, p. 235 | DOI:10.1007/s40879-022-00547-3
- Manin matrices of type C: Multi-parametric deformation, Journal of Geometry and Physics, Volume 177 (2022), p. 104523 | DOI:10.1016/j.geomphys.2022.104523
- Small modules over quantum complete intersections in two variables, Journal of Algebra and Its Applications, Volume 20 (2021) no. 03, p. 2150047 | DOI:10.1142/s021949882150047x
- Quantum Groups, q-Oscillators and q-Deformed Quantum Mechanics, Modern Perspectives in Theoretical Physics (2021), p. 91 | DOI:10.1007/978-981-15-9313-0_7
- Peter-Weyl Bases, Preferred Deformations, and Schur-Weyl Duality, Representation Theory, Mathematical Physics, and Integrable Systems, Volume 340 (2021), p. 283 | DOI:10.1007/978-3-030-78148-4_9
- The non-commutative Newton’s binomial formula in non-unital algebras and with a negative power, Bollettino dell'Unione Matematica Italiana, Volume 13 (2020) no. 1, p. 39 | DOI:10.1007/s40574-019-00200-0
- Quantizations Uq(sln+1+) and Uq(so2n+1+) as quadratic-linear algebras, Journal of Algebra, Volume 564 (2020), p. 412 | DOI:10.1016/j.jalgebra.2020.08.009
- Quantum Symmetry of Classical Spaces, Mathematical Analysis and Applications in Modeling, Volume 302 (2020), p. 101 | DOI:10.1007/978-981-15-0422-8_8
- Miraculous cancellations for quantum SL 2, Annales de la Faculté des sciences de Toulouse : Mathématiques, Volume 28 (2019) no. 3, p. 523 | DOI:10.5802/afst.1608
- Low dimensional modules over quantum complete intersections in two variables, Frontiers of Mathematics in China, Volume 14 (2019) no. 2, p. 449 | DOI:10.1007/s11464-019-0764-x
- Operator algebras in India in the past decade, Indian Journal of Pure and Applied Mathematics, Volume 50 (2019) no. 3, p. 801 | DOI:10.1007/s13226-019-0356-1
- Higher structures, quantum groups and genus zero modular operad, Journal of the London Mathematical Society, Volume 100 (2019) no. 3, p. 721 | DOI:10.1112/jlms.12217
- Hochschild cohomology of some quantum complete intersections, Journal of Algebra and Its Applications, Volume 17 (2018) no. 11, p. 1850215 | DOI:10.1142/s0219498818502158
- Koszulity and Koszul modules of dual extension algebras, Frontiers of Mathematics in China, Volume 12 (2017) no. 3, p. 583 | DOI:10.1007/s11464-016-0601-4
- The dual of a certain left quantum group, Journal of Algebra and Its Applications, Volume 15 (2016) no. 04, p. 1650072 | DOI:10.1142/s0219498816500729
- Homotopy-theoretically enriched categories of noncommutative motives, Research in the Mathematical Sciences, Volume 2 (2015) no. 1 | DOI:10.1186/s40687-015-0028-7
- Poincaré Duality for Koszul Algebras, Algebra, Geometry and Mathematical Physics, Volume 85 (2014), p. 3 | DOI:10.1007/978-3-642-55361-5_1
- Algebraic deformations of toric varieties I. General constructions, Advances in Mathematics, Volume 246 (2013), p. 33 | DOI:10.1016/j.aim.2013.06.025
- On a definition of multi-Koszul algebras, Journal of Algebra, Volume 376 (2013), p. 196 | DOI:10.1016/j.jalgebra.2012.11.030
- The coalgebra automorphism group of Hopf algebra, Journal of Pure and Applied Algebra, Volume 217 (2013) no. 10, p. 1870 | DOI:10.1016/j.jpaa.2013.01.013
- Quadratic algebras, Yang–Baxter equation, and Artin–Schelter regularity, Advances in Mathematics, Volume 230 (2012) no. 4-6, p. 2152 | DOI:10.1016/j.aim.2012.04.016
- Koszul Duality for Associative Algebras, Algebraic Operads, Volume 346 (2012), p. 61 | DOI:10.1007/978-3-642-30362-3_3
- Methods to Prove Koszulity of an Algebra, Algebraic Operads, Volume 346 (2012), p. 89 | DOI:10.1007/978-3-642-30362-3_4
- Algebras with scalar involution revisited, Journal of Pure and Applied Algebra, Volume 215 (2011) no. 12, p. 2805 | DOI:10.1016/j.jpaa.2011.04.001
- Koszul duality for monoids and the operad of enriched rooted trees, Advances in Applied Mathematics, Volume 44 (2010) no. 3, p. 261 | DOI:10.1016/j.aam.2009.05.003
- Hochschild cohomology and homology of quantum complete intersections, Algebra Number Theory, Volume 4 (2010) no. 7, p. 821 | DOI:10.2140/ant.2010.4.821
- Hopf Algebra Orbits on the Prime Spectrum of a Module Algebra, Algebras and Representation Theory, Volume 13 (2010) no. 1, p. 1 | DOI:10.1007/s10468-008-9094-5
- Algebraic properties of Manin matrices 1, Advances in Applied Mathematics, Volume 43 (2009) no. 3, p. 239 | DOI:10.1016/j.aam.2009.02.003
- The Avrunin–Scott theorem for quantum complete intersections, Journal of Algebra, Volume 322 (2009) no. 2, p. 479 | DOI:10.1016/j.jalgebra.2008.12.019
- Homology and cohomology of quantum complete intersections, Algebra Number Theory, Volume 2 (2008) no. 5, p. 501 | DOI:10.2140/ant.2008.2.501
- Generalized Operads and Their Inner Cohomomorphisms, Geometry and Dynamics of Groups and Spaces, Volume 265 (2008), p. 247 | DOI:10.1007/978-3-7643-8608-5_4
- The representation dimension of quantum complete intersections, Journal of Algebra, Volume 320 (2008) no. 1, p. 354 | DOI:10.1016/j.jalgebra.2008.04.009
- Manin matrices and Talalaev's formula, Journal of Physics A: Mathematical and Theoretical, Volume 41 (2008) no. 19, p. 194006 | DOI:10.1088/1751-8113/41/19/194006
- Non-commutative extensions of the MacMahon Master Theorem, Advances in Mathematics, Volume 216 (2007) no. 1, p. 29 | DOI:10.1016/j.aim.2007.05.020
- Multilinear forms and graded algebras, Journal of Algebra, Volume 317 (2007) no. 1, p. 198 | DOI:10.1016/j.jalgebra.2007.02.007
- Rank varieties for a class of finite-dimensional local algebras, Journal of Pure and Applied Algebra, Volume 211 (2007) no. 2, p. 497 | DOI:10.1016/j.jpaa.2007.02.006
- Yang-Mills and Some Related Algebras, Rigorous Quantum Field Theory, Volume 251 (2007), p. 65 | DOI:10.1007/978-3-7643-7434-1_6
- A Classification of Some Quadratic Algebras, Algebra Colloquium, Volume 13 (2006) no. 01, p. 133 | DOI:10.1142/s1005386706000150
- Full Graphs and Koszul Algebras I, Communications in Algebra, Volume 34 (2006) no. 11, p. 4007 | DOI:10.1080/00927870600875963
- On the Hochschild homology of quantum SL(N), Comptes Rendus. Mathématique, Volume 343 (2006) no. 1, p. 9 | DOI:10.1016/j.crma.2006.03.031
- Large Commutative Subalgebras of Quantum Algebras, Journal of Mathematical Sciences, Volume 134 (2006) no. 1, p. 1879 | DOI:10.1007/s10958-006-0091-0
- QUANTUM GROUPS AND DIFFERENTIAL FORMS, Communications in Algebra, Volume 33 (2005) no. 1, p. 253 | DOI:10.1081/agb-200040997
- On products and duality of binary, quadratic, regular operads, Journal of Pure and Applied Algebra, Volume 200 (2005) no. 3, p. 293 | DOI:10.1016/j.jpaa.2004.12.020
- Good and bad Koszul algebras and their Hochschild homology, Journal of Pure and Applied Algebra, Volume 201 (2005) no. 1-3, p. 295 | DOI:10.1016/j.jpaa.2004.12.021
- Twisted Internal coHom for Conic Algebras, Communications in Algebra, Volume 32 (2004) no. 3, p. 839 | DOI:10.1081/agb-120027954
- Energy spectrum, potential and inertia functions of a generalizedf-oscillator, Journal of Physics A: Mathematical and General, Volume 37 (2004) no. 11, p. 3707 | DOI:10.1088/0305-4470/37/11/012
- Quantum group covariant (anti)symmetrizers, -tensors, vielbein, Hodge map and Laplacian, Journal of Physics A: Mathematical and General, Volume 37 (2004) no. 39, p. 9175 | DOI:10.1088/0305-4470/37/39/009
- Twisting of homogeneous algebras, Journal of Pure and Applied Algebra, Volume 189 (2004) no. 1-3, p. 149 | DOI:10.1016/j.jpaa.2003.10.023
- The Prime and Primitive Spectra of Multiparameter Quantum Symplectic and Euclidean Spaces, Communications in Algebra, Volume 31 (2003) no. 10, p. 4713 | DOI:10.1081/agb-120023129
- Homogeneous algebras, Journal of Algebra, Volume 261 (2003) no. 1, p. 172 | DOI:10.1016/s0021-8693(02)00556-2
- COLORED YANG-BAXTER OPERATORS AND REPRESENTATIONS OF THE BRAID AND SYMMETRIC GROUPS, Communications in Algebra, Volume 30 (2002) no. 2, p. 631 | DOI:10.1081/agb-120013174
- QUANTUM MINORS ASSOCIATED TO YANG-BAXTER OPERATORS, Communications in Algebra, Volume 30 (2002) no. 2, p. 653 | DOI:10.1081/agb-120013175
- Эллиптические алгебры, Успехи математических наук, Volume 57 (2002) no. 6, p. 87 | DOI:10.4213/rm573
- Koszulity for Nonquadratic Algebras, Journal of Algebra, Volume 239 (2001) no. 2, p. 705 | DOI:10.1006/jabr.2000.8703
- Duality for exotic bialgebras, Journal of Physics A: Mathematical and General, Volume 34 (2001) no. 19, p. 4065 | DOI:10.1088/0305-4470/34/19/308
- О рядах Гильберта козюлевых алгебр, Функциональный анализ и его приложения, Volume 35 (2001) no. 2, p. 64 | DOI:10.4213/faa246
- A non-commutative binomial formula, Journal of Geometry and Physics, Volume 32 (2000) no. 4, p. 349 | DOI:10.1016/s0393-0440(99)00032-7
- Totally positive sequences andR-matrix quadratic algebras, Journal of Mathematical Sciences, Volume 100 (2000) no. 1, p. 1871 | DOI:10.1007/bf02677498
- Confluence and Koszulity, Journal of Algebra, Volume 201 (1998) no. 1, p. 243 | DOI:10.1006/jabr.1997.7249
- Down–Up Algebras, Journal of Algebra, Volume 209 (1998) no. 1, p. 305 | DOI:10.1006/jabr.1998.7511
- Free tensor categories, Journal of Mathematical Sciences, Volume 88 (1998) no. 4, p. 505 | DOI:10.1007/bf02365313
- A Nonnilpotent 1-2-Presented Graded Hopf Algebra Whose Hilbert Series Converges in the Unit Circle, Advances in Mathematics, Volume 130 (1997) no. 2, p. 161 | DOI:10.1006/aima.1997.1667
- The q-deformed vector and q-deformed outer product, International Journal of Theoretical Physics, Volume 36 (1997) no. 1, p. 5 | DOI:10.1007/bf02435766
- Duality for the Jordanian matrix quantum group, Journal of Physics A: Mathematical and General, Volume 30 (1997) no. 19, p. 6769 | DOI:10.1088/0305-4470/30/19/016
- Complete intersection dimension, Publications mathématiques de l'IHÉS, Volume 86 (1997) no. 1, p. 67 | DOI:10.1007/bf02698901
- Юрий Иванович Манин (к шестидесятилетию со дня рождения), Успехи математических наук, Volume 52 (1997) no. 4, p. 233 | DOI:10.4213/rm1595
- Representations of the virasoro-like algebra and itsq-Analog, Communications in Algebra, Volume 24 (1996) no. 14, p. 4361 | DOI:10.1080/00927879608825820
- On Clifford representation of Hopf algebras and fierz identities, Foundations of Physics, Volume 26 (1996) no. 11, p. 1457 | DOI:10.1007/bf02272367
- Free products of compact quantum groups, Communications in Mathematical Physics, Volume 167 (1995) no. 3, p. 671 | DOI:10.1007/bf02101540
- Relation between the Hilbert series of quadratic dual algebras does not imply Koszulity, Functional Analysis and Its Applications, Volume 29 (1995) no. 3, p. 213 | DOI:10.1007/bf01077062
- slq(2) realizations for Kepler and oscillator potentials and q-canonical transformations, Journal of Physics A: Mathematical and General, Volume 28 (1995) no. 8, p. 2395 | DOI:10.1088/0305-4470/28/8/029
- qanalogs of the radial Schrödinger equation inNspace dimensions, Physical Review A, Volume 52 (1995) no. 1, p. 101 | DOI:10.1103/physreva.52.101
- Postlude. A Universal Knot Invariant, Quantum Groups, Volume 155 (1995), p. 484 | DOI:10.1007/978-1-4612-0783-2_20
- A q-analog for the virasoro algebra, Communications in Algebra, Volume 22 (1994) no. 10, p. 3755 | DOI:10.1080/00927879408825052
- Quasi-hereditary algebras which are dual extensions of algebras, Communications in Algebra, Volume 22 (1994) no. 12, p. 4717 | DOI:10.1080/00927879408825097
- Contraction rule ofq-deformed Levi-Civita symbol, International Journal of Theoretical Physics, Volume 33 (1994) no. 12, p. 2291 | DOI:10.1007/bf00673957
- Quantum matrices inN dimensions, International Journal of Theoretical Physics, Volume 33 (1994) no. 4, p. 797 | DOI:10.1007/bf00672818
- The structure of Hopf algebras, Journal of Mathematical Sciences, Volume 71 (1994) no. 2, p. 2289 | DOI:10.1007/bf02111020
- BFV-BRST analysis of the classical and quantum q-deformations of the sl(2) algebra, Journal of Physics A: Mathematical and General, Volume 27 (1994) no. 1, p. 219 | DOI:10.1088/0305-4470/27/1/016
- The q-deformed Poisson bracket, Levi-Civita symbol and Poincare algebra, Journal of Physics A: Mathematical and General, Volume 27 (1994) no. 6, p. 2061 | DOI:10.1088/0305-4470/27/6/029
- Complex projective geometry and quantum projective field theory, Theoretical and Mathematical Physics, Volume 101 (1994) no. 3, p. 1387 | DOI:10.1007/bf01035459
- Le langage des espaces et des groupes quantiques, Communications in Mathematical Physics, Volume 151 (1993) no. 2, p. 275 | DOI:10.1007/bf02096770
- Some aspects of the q-deformed oscillator algebras as quantum groups, Geometric and Quantum Aspects of Integrable Systems, Volume 424 (1993), p. 213 | DOI:10.1007/bfb0021448
- Three lectures on quantum groups: representations, duality, real forms, Journal of Geometry and Physics, Volume 11 (1993) no. 1-4, p. 367 | DOI:10.1016/0393-0440(93)90065-m
- Search for minimal quantum group SUq(2) gauge field theory, Journal of Geometry and Physics, Volume 11 (1993) no. 1-4, p. 409 | DOI:10.1016/0393-0440(93)90067-o
- Elementary operations and Laplace's theorem on quantum matrices, Journal of Physics A: Mathematical and General, Volume 26 (1993) no. 17, p. 4287 | DOI:10.1088/0305-4470/26/17/034
- Two-parametric solution to graded Yang-Baxter equation and two-parametric Uuvgl(1 mod 1) algebra as a Hopf algebra, Journal of Physics A: Mathematical and General, Volume 26 (1993) no. 4, p. 935 | DOI:10.1088/0305-4470/26/4/021
- Canonical q-deformations of noncompact Lie (super-)algebras, Journal of Physics A: Mathematical and General, Volume 26 (1993) no. 6, p. 1317 | DOI:10.1088/0305-4470/26/6/015
- Duality in quantum Minkowski spacetime, Journal of Physics A: Mathematical and General, Volume 26 (1993) no. 7, p. 1691 | DOI:10.1088/0305-4470/26/7/024
- Generalized Jaynes-Cummings model with an intensity-dependent coupling interacting with a quantum group-theoretic coherent state, Physical Review A, Volume 47 (1993) no. 6, p. 5017 | DOI:10.1103/physreva.47.5017
- q-deformed Brownian motion, Physics Letters A, Volume 180 (1993) no. 1-2, p. 39 | DOI:10.1016/0375-9601(93)90491-h
- Minimum deformations of commutative algebra and linear groupGL(n), Theoretical and Mathematical Physics, Volume 95 (1993) no. 3, p. 677 | DOI:10.1007/bf01017513
- Examples of compact matrix pseudogroups arising from the twisting operation, Communications in Mathematical Physics, Volume 149 (1992) no. 1, p. 195 | DOI:10.1007/bf02096630
- The classification of differential structures on quantum 2-spheres, Communications in Mathematical Physics, Volume 150 (1992) no. 1, p. 167 | DOI:10.1007/bf02096571
- On Multigraded Differential Calculus, Groups and Related Topics (1992), p. 103 | DOI:10.1007/978-94-011-2801-8_9
- Koszul algebras of invariants, Journal of Algebra, Volume 146 (1992) no. 1, p. 85 | DOI:10.1016/0021-8693(92)90055-q
- The quantum q-deformed symmetric top: an exactly solved model, Journal of Physics A: Mathematical and General, Volume 25 (1992) no. 13, p. L781 | DOI:10.1088/0305-4470/25/13/005
- Fermionic q-oscillators and associated canonical q-transformations, Journal of Physics A: Mathematical and General, Volume 25 (1992) no. 2, p. L39 | DOI:10.1088/0305-4470/25/2/002
- On the number operators of multimode systems of deformed oscillators covariant under quantum groups, Journal of Physics A: Mathematical and General, Volume 25 (1992) no. 23, p. 6429 | DOI:10.1088/0305-4470/25/23/036
- A deformation of quantum mechanics, Journal of Physics A: Mathematical and General, Volume 25 (1992) no. 24, p. 6779 | DOI:10.1088/0305-4470/25/24/028
- Quantum symmetries associated with the Perk-Schultz model, Journal of Physics A: Mathematical and General, Volume 25 (1992) no. 7, p. 1953 | DOI:10.1088/0305-4470/25/7/034
- Quantum Groups and Non-commutative Differential Geometry, Mathematical Physics X (1992), p. 113 | DOI:10.1007/978-3-642-77303-7_9
- Quantum Groups: An Introduction and Survey for Ring Theorists, Noncommutative Rings, Volume 24 (1992), p. 131 | DOI:10.1007/978-1-4613-9736-6_6
- Quantum group realized in a symmetric-top system, Physical Review A, Volume 45 (1992) no. 7, p. 4303 | DOI:10.1103/physreva.45.4303
- Spectra of symmetric-top molecules and the quantum-deformed-symmetric-top model, Physical Review A, Volume 46 (1992) no. 3, p. 1400 | DOI:10.1103/physreva.46.1400
- Dynamics of generalized photonic fields interacting with atoms, Physical Review A, Volume 46 (1992) no. 9, p. 5865 | DOI:10.1103/physreva.46.5865
- Notes on quantum groups and quantum de Rham complexes, Theoretical and Mathematical Physics, Volume 92 (1992) no. 3, p. 997 | DOI:10.1007/bf01017077
- Quantum multilinear algebra, Tohoku Mathematical Journal, Volume 44 (1992) no. 4 | DOI:10.2748/tmj/1178227246
- The algebra of Weyl symmetrised polynomials and its quantum extension, Communications in Mathematical Physics, Volume 136 (1991) no. 3, p. 487 | DOI:10.1007/bf02099070
- Relativistic oscillator = q-oscillator, Group Theoretical Methods in Physics, Volume 382 (1991), p. 215 | DOI:10.1007/3-540-54040-7_110
- Quantum deformation of flag schemes and Grassmann schemes. I. A q-deformation of the shape-algebra for GL(n), Journal of Algebra, Volume 142 (1991) no. 1, p. 1 | DOI:10.1016/0021-8693(91)90214-s
- Representations of the quantum group SUq(2) and the little q-Jacobi polynomials, Journal of Functional Analysis, Volume 99 (1991) no. 2, p. 357 | DOI:10.1016/0022-1236(91)90045-7
- SUq(1,1) and the relativistic oscillator, Journal of Physics A: Mathematical and General, Volume 24 (1991) no. 18, p. 4283 | DOI:10.1088/0305-4470/24/18/016
- Quantum m*n-matrices and q-deformed Binet-Cauchy formula, Journal of Physics A: Mathematical and General, Volume 24 (1991) no. 21, p. L1243 | DOI:10.1088/0305-4470/24/21/001
- SUq,0(2) and SUq(2), the classical and quantum q-deformations of the SU(2) algebra. IV. Geometric quantization and Hopf algebraic structures, Journal of Physics A: Mathematical and General, Volume 24 (1991) no. 23, p. 5435 | DOI:10.1088/0305-4470/24/23/010
- Quantum superalgebra osp(2?1), Journal of Soviet Mathematics, Volume 54 (1991) no. 3, p. 923 | DOI:10.1007/bf01101123
- Representation of Quantum Groups, Mappings of Operator Algebras (1991), p. 119 | DOI:10.1007/978-1-4612-0453-4_4
- Hq(4) andSUq(2) quantum group symmetries in diatomic molecules, Physical Review A, Volume 43 (1991) no. 11, p. 6043 | DOI:10.1103/physreva.43.6043
- Diatomic-molecular spectrum in view of quantum group theory, Physical Review A, Volume 44 (1991) no. 11, p. 7405 | DOI:10.1103/physreva.44.7405
- Coherent states, K-matrix theory and q-boson realizations of the quantum algebra suq(2), Physics Letters A, Volume 153 (1991) no. 6-7, p. 303 | DOI:10.1016/0375-9601(91)90948-8
- Quantum group chiral fields and differential Yang-Baxter equations, Physics Letters B, Volume 264 (1991) no. 1-2, p. 62 | DOI:10.1016/0370-2693(91)90704-t
- Quantum group particles and non-archimedean geometry, Physics Letters B, Volume 268 (1991) no. 2, p. 179 | DOI:10.1016/0370-2693(91)90801-v
- q-Analysis and Quantum Groups, Symmetries in Science V (1991), p. 147 | DOI:10.1007/978-1-4615-3696-3_7
- Quantum deformation of compactified Minkowski space, Zeitschrift für Physik C Particles and Fields, Volume 52 (1991) no. 4, p. 583 | DOI:10.1007/bf01562332
- Relating the approaches to quantised algebras and quantum groups, Communications in Mathematical Physics, Volume 133 (1990) no. 1, p. 91 | DOI:10.1007/bf02096556
- Integrability Conditions: Recent Results in the Theory of Integrable Models, Differential Geometric Methods in Theoretical Physics, Volume 245 (1990), p. 47 | DOI:10.1007/978-1-4684-9148-7_6
- Matric bialgebras and quantum groups, Israel Journal of Mathematics, Volume 72 (1990) no. 1-2, p. 232 | DOI:10.1007/bf02764621
- A completeness relation for the q-analogue coherent states by q-integration, Journal of Physics A: Mathematical and General, Volume 23 (1990) no. 18, p. L945 | DOI:10.1088/0305-4470/23/18/002
- The quantum groups GLq(n) and Weyl-Heisenberg operators, Physics Letters B, Volume 240 (1990) no. 3-4, p. 396 | DOI:10.1016/0370-2693(90)91118-u
- Deforming maps for quantum algebras, Physics Letters B, Volume 243 (1990) no. 3, p. 237 | DOI:10.1016/0370-2693(90)90845-w
- The Quantum Group Methods of Quantising the Special Linear Group Sl(2,C), Physics, Geometry and Topology, Volume 238 (1990), p. 513 | DOI:10.1007/978-1-4615-3802-8_14
- Yang-Baxter algebra — Bethe Ansatz — conformal quantum field theories — quantum groups, Quantum Groups, Volume 370 (1990), p. 183 | DOI:10.1007/3-540-53503-9_47
- Introduction to quantum groups, Quantum Groups, Volume 370 (1990), p. 3 | DOI:10.1007/3-540-53503-9_39
- Multiparametric quantum deformation of the general linear supergroup, Communications In Mathematical Physics, Volume 123 (1989) no. 1, p. 163 | DOI:10.1007/bf01244022
- Quantum Groups and Integrable Models, Integrable Sys Quantum Field Theory (1989), p. 435 | DOI:10.1016/b978-0-12-385342-4.50019-6
- On q-analogues of the quantum harmonic oscillator and the quantum group SU(2)q, Journal of Physics A: Mathematical and General, Volume 22 (1989) no. 21, p. 4581 | DOI:10.1088/0305-4470/22/21/020
- Universal R-matrix of the quantum superalgebra osp(2 | 1), Letters in Mathematical Physics, Volume 18 (1989) no. 2, p. 143 | DOI:10.1007/bf00401868
- Hidden quantum symmetries in rational conformal field theories, Nuclear Physics B, Volume 319 (1989) no. 1, p. 155 | DOI:10.1016/0550-3213(89)90604-4
- General approach to two-dimensional critical systems, Physics Reports, Volume 184 (1989) no. 2-4, p. 121 | DOI:10.1016/0370-1573(89)90033-1
- Quantum orthogonal and symplectic groups and their embedding into quantum
, Proceedings of the Japan Academy, Series A, Mathematical Sciences, Volume 65 (1989) no. 2 | DOI:10.3792/pjaa.65.55 - Twisted canonical anticommutation relations, Reports on Mathematical Physics, Volume 27 (1989) no. 3, p. 349 | DOI:10.1016/0034-4877(89)90017-7
- Koszul duality, Journal of Geometry and Physics, Volume 5 (1988) no. 3, p. 317 | DOI:10.1016/0393-0440(88)90028-9
Cité par 151 documents. Sources : Crossref