Self-dual modules of semisimple Hopf algebras

Journal of Algebra

Volumn 257, Issue 1, 2002, Pages 88-96

  Kashina, Yevgenia ^a   Sommerhäuser, Yorck ^b   Zhu, Yongchang ^c  

^a SYRACUSE UNIVERSITY   (United States)

^b UNIVERSITY OF MUNICH   (Germany)

^c HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036873641     PISSN: 00218693     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-8693(02)00034-0     Document Type: Article

References (22)

1. S. Montgomery, Hopf Algebras and Their Actions on Rings, 2nd revised printing, in: CBMS Reg. Conf. Ser. in Math., Vol. 82, American Mathematical Society, Providence, 1997.
2. T. Kerler, Mapping class group actions on quantum doubles, Comm. Math. Phys. 168 (1995) 353-388.
3. F. Kasch, Moduln und Ringe, in: Math. Leitfaden, Teubner, Stuttgart, 1977.
4. R.G. Larson, D.E. Radford, Finite dimensional cosemisimple Hopf algebras in characteristic 0 are semisimple, J. Algebra 117 (1988) 267-289.
5. R.G. Larson, D.E. Radford, Semisimple cosemisimple Hopf algebras, Amer. J. Math. 109 (1987) 187-195.
6. P. Etingof, S. Gelaki, On the exponent of finite-dimensional Hopf algebras, Math. Res. Lett. 6 (1999) 131-140.
7. M.E. Sweedler, Integrals for Hopf algebras, Ann. Math. (2) 89 (1969) 323-335.
8. M.E. Sweedler, Hopf Algebras, Benjamin, New York, 1969.
9. V. Linchenko, S. Montgomery, A Frobenius-Schur theorem for Hopf algebras, Algebr. Represent. Theory 3 (2000) 347-355.
10. W. Burnside, On some properties of groups of odd order, Proc. London Math. Soc. (1) 33 (1900/01) 162-185.
11. W. Burnside, Theory of Groups of Finite Order, 2nd ed., Cambridge Univ. Press, Cambridge, 1911.
12. Y. Kashina, G. Mason, S. Montgomery, Computing the Frobenius-Schur indicator for abelian extensions of Hopf algebras, J. Algebra 251 (2002) 888-913.
13. I. Kaplansky, Bialgebras, in: Lecture Notes, Univ. of Chicago, Chicago, 1975.
14. Y. Sommerhäuser, On Kaplansky's conjectures, in: F. v. Oystaeyen, M. Saorin (Eds.), Interactions between Ring Theory and Representations of Algebras, in: Lecture Notes in Pure Appl. Math., Vol. 210, Dekker, New York, 2000, pp. 393-412.
15. W.D. Nichols, M.B. Richmond, The Grothendieck group of a Hopf algebra, J. Pure Appl. Algebra 106 (1996) 297-306.
16. J.P. Serre, Local Fields, in: Grad. Texts in Math., Vol. 67, Springer, Berlin, 1979.
17. P. Etingof, S. Gelaki, On finite-dimensional semisimple and cosemisimple Hopf algebras in positive characteristic, Internat. Math. Res. Notices 16 (1998) 851-864.
18. M. Gerstenhaber, On the deformation of rings and algebras, Ann. of Math. (2) 79 (1964) 59-103.
19. M.-A. Knus, Quadratic and Hermitian Forms over Rings, in: Grundlehren Math. Wiss., Vol. 294, Springer, Berlin, 1991.
20. T.Y Lam, A First Course in Noncommutative Rings, in: Grad. Texts in Math., Vol. 131, Springer, Berlin, 1991.
21. P. Bantay, The Frobenius-Schur indicator in conformal field theory, Phys. Lett. B 394 (1997) 87-88.
22. 4-symmetry of 6j-symbols and Frobenius-Schur indicators in rigid monoidal C*-categories, J. Math. Phys. 40 (1999) 408-426.