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On Relative Biexactness of Amalgamated Free Product von Neumann Algebras

2025/05/26 by Toyosawa, Kai, Yang, Zhiyuan
#FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2505.19508

Abstract

Given weakly exact tracial von Neumann algebras M1, M2 with a common injective amalgam B, we prove that the amalgamated free product M1*BM2 is biexact relative to \M1,M2\. In the case where M1 and M2 are injective, we further show that M1*BM2 is biexact relative to the amalgam B, and if B is mixing in each of M1 and M2, M1*BM2 itself is biexact. As applications, we derive structural decomposition results and subalgebra absorption theorems for amalgamated free product von Neumann algebras, extending those previously known in the group case.

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