Finite-Dimensional Kac Algebras Arising from Certain Group Actions on a Factor

International Mathematics Research Notices

Volumn , Issue 8, 1996, Pages

  Izumi, Masaki ^a   Kosaki, Hideki ^b  

^a KYOTO UNIVERSITY   (Japan)

^b KYUSHU UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

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EID: 1842588469     PISSN: 10737928     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (29)

1. S. Baaj and G. Skandalis, Unitaires multiplicatifs et dualité pour les produits croisés de C* algèbres, Ann. Sci. École Norm. Sup. (4) 26 (1993), 425-488.
2. D. Bisch and U. Haagerup, Composition of subfactors: New examples of infinite depth subfactors, to appear in Ann. Sci. École Norm. Sup.
3. J. Cuntz, "Regular actions of Hopf algebras on the C*-algebra generated by a Hubert space" in Operator Algebras, Mathematical Physics, and Low Dimensional Topology, Res. Notes Math. 5, Peters, Wellesley, Mass., 1993, 87-100.
4. M. C. David, Paragroupe d'Adrian Ocneanu et algèbre de Kac, to appear in Pacific J. Math.
5. M. Enock and J. M. Schwartz, Kac Algebras and Duality of Locally Compact Groups, Springer-Verlag, Berlin, 1992.
6. I. Hochstetter, Extensions of Hopf algebras and their cohomological description, J. Algebra 164 (1994), 267-298.
7. M. Izumi, Application of fusion rules to classification of subfactors, Publ. Res. Inst. Math. Sci. 27 (1991), 953-994.
8. _, Subalgebras of infinite C*-algebras with finite Watatani indices I. Cuntz algebras, Comm. Math. Phys. 155 (1993), 157-182.
9. _, On type II and type III graphs for subfactors, Math. Scand. 73 (1994), 307-319.
10. n, J. Funct. Anal. 112 (1993), 257-286.
11. M. Izumi and H. Kosaki, in preparation.
12. 1 factor, Mem. Amer. Math. Soc. 28 (1980), no. 237.
13. _, Index for subfactors, Invent. Math. 72 (1983), 1-25.
14. G. I. Kac, Extensions of groups to group rings, Math. USSR Sbornik 5 (1968), 451-474.
15. G. I. Kac and V. G. Paljutkin, Finite group rings, Trans. Moscow Math. Soc. (1966), 251-294; translated from Trudy Mat. Ob. 15 (1966), 224-261.
16. G. I. Kac and V. G. Paljutkin, Finite group rings, Trans. Moscow Math. Soc. (1966), 251-294; translated from Trudy Mat. Ob. 15 (1966), 224-261.
17. H. Kosaki, Sector theory and automorphisms for factor-subfactor pairs, to appear in J. Math. Soc. Japan.
18. R. Longo, Simple injective factors, Adv. Math. 63 (1987), 152-172.
19. _, A duality for Hopf algebras and subfactors I, Comm. Math. Phys. 159 (1994), 133-155.
20. S. Majid, Hopf-von Neumann algebra bicrossed products, Kac algebra bicrossed products, and the classical Yang-Baxter equation, J. Funct. Anal. 95 (1991), 291-319.
21. A. Masuoka, Semisimple Hopf algebras of dimension 2p, preprint.
22. _, Some further classification results on semi-simple Hopf algebras, preprint.
23. T. Sano, Commuting and co-commuting squares and finite dimensional Kac algebras, to appear in Pacific J. Math.
24. Y. Sekine, An example of finite dimensional Kac algebras of Kac-Paljutkin type, Proc. Amer. Math. Soc. 124 (1996), 1139-1147.
25. W. M. Singer, Extension theory for connected Hopf algebras, J. Algebra 21 (1972), 1-16.
26. C. Sutherland, Cohomology and extensions of van Neumann algebras. II, Publ. Res. Inst. Math. Sci. 16 (1980), 135-174.
27. W. Szymański, Finite index subfactors and Hopf algebra crossed products, Proc. Amer. Math. Soc. 120 (1994), 519-528.
28. M. Takeuchi, Matched pairs of groups and bismashed product of Hopf algebras, Comm. Algebra 9 (1981), 841-882.
29. G. Zeller-Meier, Produits croisés d'une C*-algèbre par un group d'automorphismes, J. Math. Pures Appl. 47 (1968), 101-239.