2019/07/20 by Nicholas Manor, Manor, Nicholas
Mathematics · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.1907.08856
openalex publication_date 2019/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is known that exactness for a discrete group is equivalent to C*-exactness, i.e., the exactness of its reduced C*-algebra. The problem of whether this equivalence holds for general locally compact groups has recently been reduced by Cave and Zacharias to the case of totally disconnected unimodular groups. We prove that the equivalence does hold for a class of groups that includes all locally compact groups with reduced C*-algebra admitting a tracial state. As a consequence, we present original proofs that totally disconnected locally compact (tdlc) invariant-neighbourhood (IN) groups and a class of groups introduced by Suzuki satisfy the equivalence problem, without using inner amenability.