Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
|
   
Available in electronic format
Available in print format
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

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

Author(s): Yoshihiro Sekine
Journal: Proc. Amer. Math. Soc. 124 (1996), 1139-1147.
MSC (1991): Primary 46L37
MathSciNet review: 1307564
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

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


References:

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


Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 46L37

Retrieve articles in all Journals with MSC (1991): 46L37


Additional Information:

Yoshihiro Sekine
Affiliation: Graduate School of Mathematics, Kyushu University, Hakozaki, Fukuoka, 812, Japan
Email: sekine@math.kyushu-u.ac.jp

DOI: 10.1090/S0002-9939-96-03199-1
PII: S 0002-9939(96)03199-1
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
Copyright of article: Copyright 1996, American Mathematical Society




AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia