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An example of finite dimensional Kac algebras
of Kac-Paljutkin type

Author: Yoshihiro Sekine
Journal: Proc. Amer. Math. Soc. 124 (1996), 1139-1147
MSC (1991): Primary 46L37
MathSciNet review: 1307564
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Abstract: An example of finite dimensional Kac algebras of Kac-Paljutkin type is given.

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  • 1. M.-C.David, Paragroupe d'Adrian Ocneanu et algebre de Kac, Pacific J. Math. (to appear).
  • 2. M.Enock and J.M.Schwartz, Une dualité dans les algèbres de von Neumann, Bull. Soc. Math. France Suppl. Mem., 44(1975),1-144. MR 56:1091
  • 3. M.Enock and J.M.Schwartz, Kac algebras and duality of locally compact groups, 1992, Springer. MR 94e:46001
  • 4. V.Jones, Index for subfactors, Invent. Math., 72(1983),1-25. MR 84d:46097
  • 5. G.I.Kac and V.G.Paljutkin, Finite ring groups, Trans. Moscow Math. Soc., (1966),251-294. MR 34:8211
  • 6. R.Longo, A duality for Hopf algebras and for subfactors, Comm. Math. Phys., 159(1994), 133-150. CMP 94:07
  • 7. S.Majid, Physics for algebraists : non-commutative and non-cocommutative Hopf algebras by a bicrossproduct construction, J. Algebra, 130(1990),17-64. MR 91j:16050
  • 8. S.Majid, Matched pairs of Lie groups associated to solutions of the Yang-Baxter equations, Pacific J. Math., 141(1990),311-332. MR 91a:17009
  • 9. S.Majid, Hopf-von Neumann algebra bicrossproducts, Kac algebra bicrossproducts, and the classical Yang-Baxter equations, J. Funct. Anal., 95(1991),291-319. MR 92b:46088
  • 10. A.Masuoka, Semisimple Hopf algebras of dimension 6, 8 , Israel J. Math. (to appear).
  • 11. A.Ocneanu, Quantized groups, string algebras and Galois theory for algebras, Operator Algebras and Applications, vol.2, London Math. Soc. Lecture Note Series Vol.136, Cambridge Univ. Press, 119-172(1988). MR 91k:46068
  • 12. A.Ocneanu, Quantum symmetry, differential geometry of finite graphs and classification of subfactors, University of Tokyo Seminary Notes 45, ( Notes recorded by Y.Kawahigashi ), 1991.
  • 13. S.Popa, Classification of subfactors : the reduction to commuting squares, Invent. Math., 101(1990),19-43. MR 91h:46109
  • 14. S.Popa, Classification of amenable subfactors of type II, Acta Math., 172(1994), 163-255. MR 95f:46105
  • 15. W.Szymanski, Finite index subfactors and Hopf algebra crossed products, Proc. Amer. Math. Soc., 120(1994),519-528. MR 94d:46061
  • 16. M.Takeuchi, Matched pairs of groups and bismash products of Hopf algebras, Comm. Algebra, 9(1981),841-882. MR 83f:16013
  • 17. T.Yamanouchi, Construction of an outer action of a finite-dimensional Kac algebra on the AFD factor of type $ II_{1} $, Inter. J. Math., 4(1993),1007-1045. MR 95c:46108

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Additional Information

Yoshihiro Sekine
Affiliation: Graduate School of Mathematics, Kyushu University, Hakozaki, Fukuoka, 812, Japan

Keywords: Kac algebra, paragroup
Received by editor(s): October 3, 1994
Additional Notes: This work was supported in part by a Grant-in-Aid for Encouragement of Young Scientists from the Ministry of Education, Science and Culture
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1996 American Mathematical Society

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