A description of amalgamated free products of finite von Neumann algebras over finite dimensional subalgebras

2009/11/11 by Dykema, Ken
#46L54 #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.0911.2052

Abstract

We show that a free product of a II₁-factor and a finite von Neumann algebra with amalgamation over a finite dimensional subalgebra is always a II₁-factor, and provide an algorithm for describing it in terms of free products (with amalgamation over the scalars) and compression/dilation. As an application, we show that the class of direct sums of finitely many von Neumann algebras that are interpolated free group factors, hyperfinite II₁-factors, type I_n algebras for n finite, and finite dimensional algebras, is closed under taking free products with amalgamation over finite dimensional subalgebras.

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