2008/12/01 by Don Hadwin, Hadwin, Don, Jiankui Li +5 · 1 citation
Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Geometric and Algebraic Topology #Operator Algebras (math.OA) #Random Matrices and Applications #math.OA
paper · pdf · doi:10.48550/arxiv.0812.0189
29 pages
arxiv created 2008/12/01 · openalex publication_date 2008/12/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the paper, we prove that reduced free products of unital AH algebras with respect to given faithful tracial states, in the sense of Voiculescu, are Blackadar and Kirhcberg's MF algebras. We also show that the reduced free products of unital AH algebras with respect to given faithful tracial states, under mild conditions, are not quasidiagonal. Therefore we conclude, for a large class of AH algebras, the Brown-Douglas-Fillmore extension semigroups of the reduced free products of these AH algebras with respect to given faithful tracial states are not groups. Our result is based on Haagerup and Thorbjørsen's work on the reduced C^*-algebras of free groups.