A note on unital full amalgamated free products of quasi-diagonal C*-algebras

2014/11/29 by Qihui Li, Li, Qihui, Don Hadwin +7
Mathematics · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.1412.0120

openalex publication_date 2014/11/29 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In the paper, we consider the question whether a unital full amalgamated free product of quasidiagonal C*-algebras is quasidiagonal again. We give a sufficient condition such that a unital full amalgamated free product of quasidiagonal C*-algebras with amalgamation over a finite dimensional C*- algebra is quasidiagonal. Applying this result, we conclude that a unital full free product of two AF algebras with amalgamation over a finite-dimensional C*-algebra is AF if there are faithful tracial states on each of these two AF algebras such that the restrictions on the common subalgebra agree.

Citations

• Pullback and Pushout Constructions in C*-Algebra Theory

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