On Central Sequence Algebras of Tensor Product von Neumann Algebras

Abstract

We show that when M , N_{1} , N_{2} are tracial von Neumann algebras with M'\cap M^{\omega} abelian, M'\cap(M\bar \otimes N_{1})^{\omega} and M'\cap(M\bar \otimes N_{2})^{\omega} commute in (M\bar \otimes N_{1}\bar \otimes N_{2})^{\omega} . As a consequence, we obtain information on McDuff decomposition of II _{1} factors of the form M\bar \otimes N , where M is a non-McDuff factor.