Conjugate Pairs of Subfactors and Entropy for Automorphisms

Details Conjugate Pairs of Subfactors and Entropy for Automorphisms Conjugate Pairs of Subfactors and Entropy for Automorphisms

2010-02-03

arxiv.org/abs/1002.0631v1

International Journal of Mathematics, Vol. 22, No. 4 (2011) 577--592

Mathematics

Operator Algebras

20 pages

Scientific paper

Based on the fact that, for a subfactor $N$ of a II$_1$ factor $M,$ the first non-trivial Jones index is 2 and then $M$ is decomposed as the crossed product of $N$ by an outer action of ${\mathbb{Z}}_2,$ we study pairs $ \{N, uNu^* \}$ from a view point of entropy for two subalgebras of $M$ with a connection to the entropy for automorphisms, where the inclusion of II$_1$ factors $ N \subset M$ is given as $M$ is the crossed product of $N$ by a finite group of outer automorphisms and $u$ is a unitary in $M.$

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