Degenerations for representations of quivers with relations
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 19 (1986) no. 2, pp. 275-301.
@article{ASENS_1986_4_19_2_275_0,
     author = {Riedtmann, Christine},
     title = {Degenerations for representations of quivers with relations},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {275--301},
     publisher = {Elsevier},
     volume = {Ser. 4, 19},
     number = {2},
     year = {1986},
     doi = {10.24033/asens.1508},
     mrnumber = {88b:16051},
     zbl = {0603.16025},
     language = {en},
     url = {https://www.numdam.org/articles/10.24033/asens.1508/}
}
TY  - JOUR
AU  - Riedtmann, Christine
TI  - Degenerations for representations of quivers with relations
JO  - Annales scientifiques de l'École Normale Supérieure
PY  - 1986
SP  - 275
EP  - 301
VL  - 19
IS  - 2
PB  - Elsevier
UR  - https://www.numdam.org/articles/10.24033/asens.1508/
DO  - 10.24033/asens.1508
LA  - en
ID  - ASENS_1986_4_19_2_275_0
ER  - 
%0 Journal Article
%A Riedtmann, Christine
%T Degenerations for representations of quivers with relations
%J Annales scientifiques de l'École Normale Supérieure
%D 1986
%P 275-301
%V 19
%N 2
%I Elsevier
%U https://www.numdam.org/articles/10.24033/asens.1508/
%R 10.24033/asens.1508
%G en
%F ASENS_1986_4_19_2_275_0
Riedtmann, Christine. Degenerations for representations of quivers with relations. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 19 (1986) no. 2, pp. 275-301. doi : 10.24033/asens.1508. https://www.numdam.org/articles/10.24033/asens.1508/

[1] S. Abeasis and A. Del Fra, Degenerations for the representations of a quiver of type Am (J. of Algebra, Vol. 93, 1985, pp. 376-412). | MR | Zbl

[2] S. Abeasis and A. Del Fra, Degenerations for the representations of an equioriented quiver of type Dm (Adv. Math., Vol. 52, 1984, pp. 81-172). | MR | Zbl

[3] M. Auslander and I. Reiten, Representation theory of Artin algebras IV (Comm. Algebra, Vol. 5 (5), 1977, pp. 443-518). | MR | Zbl

[4] K. Bongartz and P. Gabriel, Covering spaces in representation theory (Invent. Math., Vol. 65, 1982, pp. 331-378). | MR | Zbl

[5] P. Gabriel, Auslander-Reiten sequences and representation-finite algebras, in "Representation Theory I" (Springer Lecture Notes, Vol. 831, 1980, pp. 1-71). | MR | Zbl

[6] W. Hesselink, Singularities in the nilpotent scheme of a classical group (TAMS, Vol. 222, 1976, pp. 1-32). | MR | Zbl

[7] H. Kraft, Geometrische Methoden in der Invariantentheorie. Aspekte der Mathematik, Vieweg, 1984. | MR | Zbl

[8] Ch. Riedtmann, Representation finite selfinjective algebras of class An, in "Representation Theory II" (Springer Lecture Notes, Vol. 832, 1980, pp. 449-520). | MR | Zbl

[9] Ch. Riedtmann, On stable blocks of Auslander-algebras (TAMS, Vol. 238, 1984, pp. 485-505). | MR | Zbl

  • Derksen, Harm; Klep, Igor; Makam, Visu; Volčič, Jurij Ranks of linear matrix pencils separate simultaneous similarity orbits, Advances in Mathematics, Volume 415 (2023), p. 108888 | DOI:10.1016/j.aim.2023.108888
  • Suárez-Álvarez, Mariano A Simple Homological Characterization of String Algebras of Finite Representation Type, Algebras and Representation Theory, Volume 26 (2023) no. 5, p. 1759 | DOI:10.1007/s10468-022-10154-1
  • Bobiński, Grzegorz; Zwara, Grzegorz Tangent Spaces of Orbit Closures for Representations of Dynkin Quivers of Type D, Algebras and Representation Theory, Volume 26 (2023) no. 5, p. 1951 | DOI:10.1007/s10468-022-10160-3
  • Lu, Ming; Wang, Weiqiang Hall algebras and quantum symmetric pairs I: Foundations, Proceedings of the London Mathematical Society, Volume 124 (2022) no. 1, p. 1 | DOI:10.1112/plms.12423
  • Bobiński, Grzegorz Algebras with Irreducible Module Varieties III: Birkhoff Varieties, International Mathematics Research Notices, Volume 2021 (2021) no. 4, p. 2497 | DOI:10.1093/imrn/rnz192
  • Erdmann, Karin; Gratz, Sira; Lamberti, Lisa Cluster tilting modules for mesh algebras, Linear Algebra and its Applications, Volume 630 (2021), p. 112 | DOI:10.1016/j.laa.2021.07.021
  • SAORÍN, MANUEL; ZIMMERMANN, ALEXANDER DEGENERATING 0 IN TRIANGULATED CATEGORIES, Nagoya Mathematical Journal, Volume 244 (2021), p. 158 | DOI:10.1017/nmj.2020.10
  • Bate, Michael; Martin, Benjamin; Röhrle, Gerhard Semisimplification for subgroups of reductive algebraic groups, Forum of Mathematics, Sigma, Volume 8 (2020) | DOI:10.1017/fms.2020.30
  • Smirnov, E. Yu. Multiple Flag Varieties, Journal of Mathematical Sciences, Volume 248 (2020) no. 3, p. 338 | DOI:10.1007/s10958-020-04875-1
  • Saorín, Manuel; Zimmermann, Alexander Symmetry of the Definition of Degeneration in Triangulated Categories, Algebras and Representation Theory, Volume 22 (2019) no. 4, p. 801 | DOI:10.1007/s10468-018-9799-z
  • Hiramatsu, Naoya; Takahashi, Ryo; Yoshino, Yuji Degenerations over (A∞)-singularities and construction of degenerations over commutative rings, Journal of Algebra, Volume 525 (2019), p. 374 | DOI:10.1016/j.jalgebra.2018.12.031
  • Takahashi, Ryo On the transitivity of degeneration of modules, manuscripta mathematica, Volume 159 (2019) no. 3-4, p. 431 | DOI:10.1007/s00229-018-1076-2
  • Kaniecki, Mariusz; Kosakowska, Justyna; Schmidmeier, Markus Operations on arc diagrams and degenerations for invariant subspaces of linear operators. Part II, Communications in Algebra, Volume 46 (2018) no. 5, p. 2243 | DOI:10.1080/00927872.2017.1376212
  • Hiramatsu, Naoya On the stable hom relation and stable degenerations of Cohen–Macaulay modules, Journal of Pure and Applied Algebra, Volume 222 (2018) no. 9, p. 2609 | DOI:10.1016/j.jpaa.2017.10.010
  • Kosakowska, Justyna; Schmidmeier, Markus The boundary of the irreducible components for invariant subspace varieties, Mathematische Zeitschrift, Volume 290 (2018) no. 3-4, p. 953 | DOI:10.1007/s00209-018-2047-8
  • Nornes, Nils M.; Oppermann, Steffen Degenerations of Submodules and Composition Series, Algebras and Representation Theory, Volume 20 (2017) no. 4, p. 803 | DOI:10.1007/s10468-017-9677-0
  • Wang, Zhengfang Triangle Order ≤△ in Singular Categories, Algebras and Representation Theory, Volume 19 (2016) no. 2, p. 397 | DOI:10.1007/s10468-015-9579-y
  • Saorín, Manuel; Zimmermann, Alexander An Axiomatic Approach for Degenerations in Triangulated Categories, Applied Categorical Structures, Volume 24 (2016) no. 4, p. 385 | DOI:10.1007/s10485-015-9401-3
  • Gesmundo, Fulvio Geometric aspects of Iterated Matrix Multiplication, Journal of Algebra, Volume 461 (2016), p. 42 | DOI:10.1016/j.jalgebra.2016.04.028
  • Bleher, Frauke M.; Chinburg, Ted; Huisgen-Zimmermann, Birge Orbit closures and rational surfaces, Journal of Pure and Applied Algebra, Volume 220 (2016) no. 5, p. 1785 | DOI:10.1016/j.jpaa.2015.10.002
  • Muchtadi-Alamsyah, Intan, 2015 International Conference on Research and Education in Mathematics (ICREM7) (2015), p. 238 | DOI:10.1109/icrem.2015.7357061
  • Darmajid; Jensen, Bernt Tore Varieties of complexes of fixed rank, Journal of Algebra and Its Applications, Volume 14 (2015) no. 05, p. 1550077 | DOI:10.1142/s0219498815500772
  • Hiramatsu, Naoya Degenerations of graded Cohen-Macaulay modules, Journal of Commutative Algebra, Volume 7 (2015) no. 2 | DOI:10.1216/jca-2015-7-2-221
  • Derksen, H.; Huisgen-Zimmermann, B.; Weyman, J. Top-stable degenerations of finite dimensional representations II, Advances in Mathematics, Volume 259 (2014), p. 730 | DOI:10.1016/j.aim.2014.02.008
  • Armour, Aaron; Zhang, Yinhuo Geometric Classification of 4-Dimensional Superalgebras, Algebra, Geometry and Mathematical Physics, Volume 85 (2014), p. 291 | DOI:10.1007/978-3-642-55361-5_18
  • Malicki, Piotr; de la Peña, José A.; Skowroński, Andrzej Cycle-Finite Module Categories, Algebras, Quivers and Representations, Volume 8 (2013), p. 209 | DOI:10.1007/978-3-642-39485-0_10
  • Bekkert, Viktor; Drozd, Yuriy; Futorny, Vyacheslav Tilting, deformations and representations of linear groups over Euclidean algebras, Journal of Pure and Applied Algebra, Volume 217 (2013) no. 6, p. 1141 | DOI:10.1016/j.jpaa.2012.09.031
  • Hiramatsu, Naoya; Yoshino, Yuji Examples of degenerations of Cohen-Macaulay modules, Proceedings of the American Mathematical Society, Volume 141 (2013) no. 7, p. 2275 | DOI:10.1090/s0002-9939-2013-11523-6
  • Bongartz, Klaus; Frank, Guido; Wolters, Isabel On minimal disjoint degenerations of modules over tame path algebras, Advances in Mathematics, Volume 226 (2011) no. 2, p. 1875 | DOI:10.1016/j.aim.2010.09.002
  • Riedtmann, Ch.; Rutscho, M.; Smalø, S.O. Irreducible components of module varieties: An example, Journal of Algebra, Volume 331 (2011) no. 1, p. 130 | DOI:10.1016/j.jalgebra.2010.11.009
  • Yoshino, Yuji Stable degenerations of Cohen–Macaulay modules, Journal of Algebra, Volume 332 (2011) no. 1, p. 500 | DOI:10.1016/j.jalgebra.2010.11.005
  • Bobiński, Grzegorz Canonical Tilting Modules Over Shod Algebras are Regular in Codimension One, Communications in Algebra, Volume 38 (2010) no. 7, p. 2454 | DOI:10.1080/00927870903399968
  • Forbregd, Tore A.; Nornes, Nils M.; Smalø, Sverre O. Partial orders on representations of algebras, Journal of Algebra, Volume 323 (2010) no. 7, p. 2058 | DOI:10.1016/j.jalgebra.2009.12.031
  • Materna, Stéphane Quiver representations with an irreducible null cone, Journal of Algebra, Volume 324 (2010) no. 10, p. 2832 | DOI:10.1016/j.jalgebra.2010.05.028
  • Deng, Bangming; Du, Jie Tight monomials and the monomial basis property, Journal of Algebra, Volume 324 (2010) no. 12, p. 3355 | DOI:10.1016/j.jalgebra.2010.09.022
  • Malicki, Piotr Degenerations for indecomposable modules in almost cyclic coherent Auslander–Reiten components, Journal of Pure and Applied Algebra, Volume 214 (2010) no. 10, p. 1701 | DOI:10.1016/j.jpaa.2009.12.013
  • Jensen, Bernt; Madsen, Dag; Su, Xiuping Degeneration of A-infinity modules, Transactions of the American Mathematical Society, Volume 361 (2009) no. 8, p. 4125 | DOI:10.1090/s0002-9947-09-04693-5
  • Huisgen-Zimmermann, Birge Classifying representations by way of Grassmannians, Transactions of the American Mathematical Society, Volume 359 (2007) no. 6, p. 2687 | DOI:10.1090/s0002-9947-07-03997-9
  • Zwara, Grzegorz Codimension two singularities for representations of extended Dynkin quivers, manuscripta mathematica, Volume 123 (2007) no. 3, p. 237 | DOI:10.1007/s00229-007-0093-3
  • Smal⊘, S. O.; Valenta, A. Finitely Presented Functors and Degenerations#, Communications in Algebra, Volume 34 (2006) no. 5, p. 1861 | DOI:10.1080/00927870500542838
  • Geiß, Christof; Leclerc, Bernard; Schröer, Jan Rigid modules over preprojective algebras, Inventiones mathematicae, Volume 165 (2006) no. 3, p. 589 | DOI:10.1007/s00222-006-0507-y
  • Bongartz, Klaus; Kettler, Michael; Riedtmann, Christine On module categories where the hom-order and the stable hom-relation coincide, Journal of Algebra, Volume 299 (2006) no. 1, p. 219 | DOI:10.1016/j.jalgebra.2005.06.025
  • Olbricht, Roland On degenerations between preprojective modules over wild quivers, Journal of Algebra, Volume 306 (2006) no. 2, p. 439 | DOI:10.1016/j.jalgebra.2006.09.015
  • SmalØ, S. O.; Valenta, A. Degenerations of k[t]/(tr)-Modules Giving Stratification of the Orbits, Algebras and Representation Theory, Volume 8 (2005) no. 2, p. 249 | DOI:10.1007/s10468-005-3604-5
  • Kettler, Michael Degenerations and Stable Homomorphisms#, Communications in Algebra, Volume 33 (2005) no. 10, p. 3739 | DOI:10.1080/00927870500243221
  • Sato, Masahisa; Ohnuki, Yosuke On Degenerations and Splitting of Exact Sequences, Communications in Algebra, Volume 33 (2005) no. 7, p. 2281 | DOI:10.1081/agb-200063590
  • Zwara, Grzegorz Regularity in codimension one of orbit closures in module varieties, Journal of Algebra, Volume 283 (2005) no. 2, p. 821 | DOI:10.1016/j.jalgebra.2004.09.021
  • JENSEN, BERNT TORE; SU, XIUPING; ZIMMERMANN, ALEXANDER DEGENERATION-LIKE ORDERS IN TRIANGULATED CATEGORIES, Journal of Algebra and Its Applications, Volume 04 (2005) no. 05, p. 587 | DOI:10.1142/s021949880500137x
  • Magyar, Peter Bruhat Order for Two Flags and a Line, Journal of Algebraic Combinatorics, Volume 21 (2005) no. 1, p. 71 | DOI:10.1007/s10801-005-6281-x
  • Jensen, Bernt Tore; Su, Xiuping; Zimmermann, Alexander Degenerations for derived categories, Journal of Pure and Applied Algebra, Volume 198 (2005) no. 1-3, p. 281 | DOI:10.1016/j.jpaa.2004.10.001
  • Aehle, Robert The complexity of minimal degenerations for representation-finite selfinjective algebras, Journal of Algebra, Volume 274 (2004) no. 2, p. 652 | DOI:10.1016/s0021-8693(03)00524-6
  • Kosakowska, Justyna Degenerations in a class of matrix varieties and prinjective modules, Journal of Algebra, Volume 263 (2003) no. 2, p. 262 | DOI:10.1016/s0021-8693(03)00173-x
  • Riedtmann, Christine Degenerations for nonstandard algebras, Journal of Algebra, Volume 255 (2002) no. 2, p. 342 | DOI:10.1016/s0021-8693(02)00133-3
  • Zwara, Grzegorz Tame Algebras and Degenerations of Modules, Infinite Length Modules (2000), p. 311 | DOI:10.1007/978-3-0348-8426-6_16
  • Magyar, Peter; Weyman, Jerzy; Zelevinsky, Andrei Multiple Flag Varieties of Finite Type, Advances in Mathematics, Volume 141 (1999) no. 1, p. 97 | DOI:10.1006/aima.1998.1776
  • Brüstle, T.; Hille, L.; Röhrle, G.; Zwara, G. The Bruhat–Chevalley Order of Parabolic Group Actions in General Linear Groups and Degeneration for Δ-Filtered Modules, Advances in Mathematics, Volume 148 (1999) no. 2, p. 203 | DOI:10.1006/aima.1999.1851
  • Reineke, Markus Multiplicative properties of dual canonical bases of quantum groups, Journal of Algebra, Volume 211 (1999) no. 1, p. 134 | DOI:10.1006/jabr.1998.7570
  • Zwara, Grzegorz Degenerations for modules over representation-finite algebras, Proceedings of the American Mathematical Society, Volume 127 (1999) no. 5, p. 1313 | DOI:10.1090/s0002-9939-99-04714-0
  • Edelman, Alan; Elmroth, Erik; Kågström, Bo A Geometric Approach to Perturbation Theory of Matrices and Matrix Pencils. Part II: A Stratification-Enhanced Staircase Algorithm, SIAM Journal on Matrix Analysis and Applications, Volume 20 (1999) no. 3, p. 667 | DOI:10.1137/s0895479896310184
  • Zwara, Grzegorz Degenerations for Modules over Representation-Finite Biserial Algebras, Journal of Algebra, Volume 198 (1997) no. 2, p. 563 | DOI:10.1006/jabr.1997.7160
  • Bongartz, Klaus Minimal singularities for representations of Dynkin quivers, Commentarii Mathematici Helvetici, Volume 69 (1994) no. 1, p. 575 | DOI:10.1007/bf02564505
  • Bongartz, Klaus A geometric version of the Morita equivalence, Journal of Algebra, Volume 139 (1991) no. 1, p. 159 | DOI:10.1016/0021-8693(91)90288-j

Cité par 62 documents. Sources : Crossref