no. 1
Finite quantum groups over abelian groups of prime exponent
Andruskiewitsch, Nicolás ; Schneider, Hans-Jürgen1
1 Universität München, Mathematisches Institut, Theresienstr. 39, 80333 Munich (Allemagne)
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 35 (2002) no. 1, pp. 1-26.
DOI : 10.1016/s0012-9593(01)01082-5
Andruskiewitsch, Nicolás  ; Schneider, Hans-Jürgen 1

1 Universität München, Mathematisches Institut, Theresienstr. 39, 80333 Munich (Allemagne) 
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     title = {Finite quantum groups over abelian groups of prime exponent},
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Andruskiewitsch, Nicolás; Schneider, Hans-Jürgen. Finite quantum groups over abelian groups of prime exponent. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 35 (2002) no. 1, pp. 1-26. doi : 10.1016/s0012-9593(01)01082-5. http://www.numdam.org/articles/10.1016/s0012-9593(01)01082-5/

[1] Andersen H.H., Jantzen J., Soergel W., Representations of quantum groups at a pth root of unity and of semisimple groups in characteristic p: Independence of p, Astérisque, 220, 1994. | Numdam | MR | Zbl

[2] Andruskiewitsch N., Dăscălescu S, On quantum groups at −1, Algebr. Represent. Theory, to appear. | Zbl

[3] Andruskiewitsch N., Graña M., Braided Hopf algebras over non-abelian groups, Bol. Acad. Ciencias (Córdoba) 63 (1999) 45-78, available at www.mate.uncor.edu/andrus/articulos.html. | MR | Zbl

[4] Andruskiewitsch N., Schneider H.-J., Lifting of quantum linear spaces and pointed Hopf algebras of order p3, J. Algebra 209 (1998) 658-691. | MR | Zbl

[5] Andruskiewitsch N., Schneider H.-J., Finite quantum groups and Cartan matrices, Adv. in Math. 154 (2000) 1-45. | MR | Zbl

[6] Andruskiewitsch N., Schneider H.-J., Lifting of Nichols algebras of type A2 and pointed Hopf algebras of order p4, in: Caenepeel S. (Ed.), Proceedings of the Colloquium in Brussels 1998, Hopf Algebras and Quantum Groups, Marcel Dekker, 2000, pp. 1-18. | MR | Zbl

[7] Andruskiewitsch N., Schneider H.-J., Pointed Hopf algebras, in: New Directions in Hopf Algebras, MSRI Series Cambridge Univ. Press, to appear. | MR | Zbl

[8] Beattie M., Dăscălescu S., Grünenfelder L., On the number of types of finite-dimensional Hopf algebras, Inventiones Math. 136 (1999) 1-7. | MR | Zbl

[9] Beattie M., Dăscălescu S., Raianu S., Lifting of Nichols algebras of type B2, Preprint, 2001.

[10] Caenepeel S., Dăscălescu S., Pointed Hopf algebras of dimension p3, J. Algebra 209 (1998) 622-634. | MR | Zbl

[11] Caenepeel S., Dăscălescu S., Raianu S., Classifying pointed Hopf algebras of dimension 16, Comm. Algebra 28 (2000) 541-568. | MR | Zbl

[12] De Concini C., Procesi C., Quantum groups, in: D-modules, Representation Theory and Quantum Groups, Lecture Notes in Maths., 1565, Springer-Verlag, 1993, pp. 31-140. | MR | Zbl

[13] Didt D., Linkable Dynkin diagrams, Preprint, 2001. | MR

[14] Doi Y., Takeuchi M., Multiplication alteration by two-cocycles. The quantum version, Comm. Algebra 22 (14) (1994) 5715-5732. | MR | Zbl

[15] Drinfeld V.G., Quasi-Hopf algebras, Leningrad Math. J. 1 (1990) 1419-1457. | MR

[16] Gelaki S., On pointed Hopf algebras and Kaplansky's tenth conjecture, J. Algebra 209 (1998) 635-657. | MR | Zbl

[17] Graña M., Pointed Hopf algebras of dimension 32, Comm. Algebra 28 (2000) 2935-2976. | MR | Zbl

[18] Graña M., On Pointed Hopf algebras of dimension p5, Glasgow Math. J. 42 (2000) 405-419. | MR | Zbl

[19] Graña M., On Nichols algebras of low dimension, Contemp. Math. 267 (2000) 111-134. | MR | Zbl

[20] Kac V., Infinite Dimensional Lie Algebras, Cambridge Univ. Press, 1995. | MR | Zbl

[21] Lusztig G., Finite dimensional Hopf algebras arising from quantized universal enveloping algebras, J. Amer. Math. Soc. 3, 257-296. | MR | Zbl

[22] Lusztig G., Quantum groups at roots of 1, Geom. Dedicata 35 (1990) 89-114. | MR | Zbl

[23] Lusztig G., Introduction to Quantum Groups, Birkhäuser, 1993. | MR | Zbl

[24] Majid S., Crossed products by braided groups and bosonization, J. Algebra 163 (1994) 165-190. | MR | Zbl

[25] Masuoka A., Defending the negated Kaplansky conjecture, Proc. Amer. Math. Soc. 129 (2001) 3185-3192. | MR | Zbl

[26] Montgomery S., Hopf Algebras and Their Actions on Rings, CBMS Lecture Notes, 82, American Mathematical Society, 1993. | MR | Zbl

[27] Müller E., Some topics on Frobenius-Lusztig kernels, I, J. Algebra 206 (1998) 624-658. | MR | Zbl

[28] Musson I., Finite quantum groups and pointed Hopf algebras, Preprint, 1999. | MR

[29] Nichols W.D., Bialgebras of type one, Comm. Algebra 6 (1978) 1521-1552. | MR | Zbl

[30] Nichols W.D., Zoeller M.B., A Hopf algebra freeness theorem, Amer. J. Math. 111 (1989) 381-385. | MR | Zbl

[31] Radford D., Hopf algebras with projection, J. Algebra 92 (1985) 322-347. | MR | Zbl

[32] Ringel C., PBW-bases of quantum groups, J. Reine Angew. Math. 470 (1996) 51-88. | MR | Zbl

[33] Rosso M., Groupes quantiques et algèbres de battage quantiques, C.R.A.S. (Paris) 320 (1995) 145-148. | MR | Zbl

[34] Rosso M., Quantum groups and quantum shuffles, Inventiones Math. 133 (1998) 399-416. | MR | Zbl

[35] Schauenburg P., A characterization of the Borel-like subalgebras of quantum enveloping algebras, Comm. Algebra 24 (1996) 2811-2823. | MR | Zbl

[36] Stefan D., Van Oystaeyen F., Hochschild cohomology and coradical filtration of pointed Hopf algebras, J. Algebra 210 (1998) 535-556. | MR | Zbl

[37] Woronowicz S.L., Differential calculus on compact matrix pseudogroups (quantum groups), Comm. Math. Phys. 122 (1989) 125-170. | MR | Zbl

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