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

Sekine, Yoshihiro

doi:10.1090/S0002-9939-96-03199-1

An example of finite dimensional Kac algebras of Kac-Paljutkin type
HTML articles powered by AMS MathViewer

by Yoshihiro Sekine PDF

Proc. Amer. Math. Soc. 124 (1996), 1139-1147 Request permission

Abstract:

An example of finite dimensional Kac algebras of Kac-Paljutkin type is given.

References

M.-C.David, Paragroupe d’Adrian Ocneanu et algebre de Kac, Pacific J. Math. (to appear).
Michel Enock and Jean-Marie Schwartz, Une dualité dans les algèbres de von Neumann, Supplément au Bull. Soc. Math. France, Tome 103, no. 4, Société Mathématique de France, Paris, 1975 (French). Bull. Soc. Math. France Mém., No. 44. MR 0442710
Michel Enock and Jean-Marie Schwartz, Kac algebras and duality of locally compact groups, Springer-Verlag, Berlin, 1992. With a preface by Alain Connes; With a postface by Adrian Ocneanu. MR 1215933, DOI 10.1007/978-3-662-02813-1
V. F. R. Jones, Index for subfactors, Invent. Math. 72 (1983), no. 1, 1–25. MR 696688, DOI 10.1007/BF01389127
G. I. Kac and V. G. Paljutkin, Finite ring groups, Trudy Moskov. Mat. Obšč. 15 (1966), 224–261 (Russian). MR 0208401
R.Longo, A duality for Hopf algebras and for subfactors, Comm. Math. Phys., 159(1994), 133-150.
Shahn Majid, Physics for algebraists: noncommutative and noncocommutative Hopf algebras by a bicrossproduct construction, J. Algebra 130 (1990), no. 1, 17–64. MR 1045735, DOI 10.1016/0021-8693(90)90099-A
Shahn Majid, Matched pairs of Lie groups associated to solutions of the Yang-Baxter equations, Pacific J. Math. 141 (1990), no. 2, 311–332. MR 1035446
Shahn Majid, Hopf-von Neumann algebra bicrossproducts, Kac algebra bicrossproducts, and the classical Yang-Baxter equations, J. Funct. Anal. 95 (1991), no. 2, 291–319. MR 1092128, DOI 10.1016/0022-1236(91)90031-Y
A.Masuoka, Semisimple Hopf algebras of dimension 6, 8 , Israel J. Math. (to appear).
Adrian Ocneanu, Quantized groups, string algebras and Galois theory for algebras, Operator algebras and applications, Vol. 2, London Math. Soc. Lecture Note Ser., vol. 136, Cambridge Univ. Press, Cambridge, 1988, pp. 119–172. MR 996454
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.
S. Popa, Classification of subfactors: the reduction to commuting squares, Invent. Math. 101 (1990), no. 1, 19–43. MR 1055708, DOI 10.1007/BF01231494
Sorin Popa, Classification of amenable subfactors of type II, Acta Math. 172 (1994), no. 2, 163–255. MR 1278111, DOI 10.1007/BF02392646
Wojciech Szymański, Finite index subfactors and Hopf algebra crossed products, Proc. Amer. Math. Soc. 120 (1994), no. 2, 519–528. MR 1186139, DOI 10.1090/S0002-9939-1994-1186139-1
Mitsuhiro Takeuchi, Matched pairs of groups and bismash products of Hopf algebras, Comm. Algebra 9 (1981), no. 8, 841–882. MR 611561, DOI 10.1080/00927878108822621
Takehiko Yamanouchi, Construction of an outer action of a finite-dimensional Kac algebra on the AFD factor of type $\textrm {II}_1$, Internat. J. Math. 4 (1993), no. 6, 1007–1045. MR 1250260, DOI 10.1142/S0129167X93000479