Amenability for unitary groups of C*-algebras

2023/05/22 by Alekseev, Vadim, Schmidt, Max, Thom, Andreas
#43A07 #46L99 #FOS: Mathematics #Group Theory (math.GR) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2305.13181

Abstract

In this note we state a conjecture that characterizes unital C*-algebras for which the unitary group is amenable as a topological group in the norm topology. We prove the conjecture for simple, separable, stably finite, unital, \mathcal Z-stable, UCT C*-algebras with torsionfree K₀ using the progress on the Elliott classification program for nuclear C*-algebras as well as Pestov's study of amenability of gauge groups. Based on work of Kirchberg, we provide a counterexample to a question of Ng, who proposed a different characterization in earlier work.

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