Institute of Mathematics for Industry

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Unique prime factorization and bicentralizer problem for a class of type III factors


Hold Date 2015-06-01 16:30~2015-06-01 18:00

Place Seminar Room 1, Faculty of Mathematics building, Ito Campus

Object person  

Speaker Yusuke ISONO (RIMS, Kyoto University)

Abstract:
We introduce the class C_(AO) of von Neumann algebras that particularly contains free (quantum) group factors and free Araki-Woods factors. We show that any tensor product factor, which consists of finitely many factors in C_(AO), retains each tensor component (up to stable isomorphism). This generalizes Ozawa-Popa's pioneering work for free group factors and provides a new result for free Araki-Woods factors. In order to obtain this, we show that Connes's bicentralizer problem has a positive solution for all type III_1 factors in the class C_(AO). This is joint work with C. Houdayer.