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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Finite index subfactors and Hopf algebra crossed products


Author: Wojciech Szymański
Journal: Proc. Amer. Math. Soc. 120 (1994), 519-528
MSC: Primary 46L37; Secondary 16W30
MathSciNet review: 1186139
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Abstract: We show that if $ {\mathbf{N}} \subseteq {\mathbf{M}} \subseteq {\mathbf{L}} \subseteq {\mathbf{K}}$ is a Jones's tower of type $ {\text{I}}{{\text{I}}_1}$ factors satisfying $ [{\mathbf{M}}:{\mathbf{N}}] < \infty ,\;{\mathbf{N}}' \cap {\mathbf{M}} = \mathbb{C}I,\;{\mathbf{N}}' \cap {\mathbf{K}}$ a factor, then $ {\mathbf{M}}' \cap {\mathbf{K}}$ bears a natural Hopf $ {\ast}$-algebra structure and there is an action of $ {\mathbf{M}}' \cap {\mathbf{K}}$ on $ {\mathbf{L}}$ such that the resulting crossed product is isomorphic to $ {\mathbf{K}}$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1186139-1
PII: S 0002-9939(1994)1186139-1
Keywords: Derived tower, Hopf algebra action and crossed product, Jones's index, subfactor of a type $ {\text{I}}{{\text{I}}_1}$ factor
Article copyright: © Copyright 1994 American Mathematical Society