Semigroup C*-algebras arising from graphs of monoids

Cheng Chen

Monday 12th December, 2022 14:00-15:00 Maths 311B


In the talk, I will introduce a class of graphs of monoids and their semigroup C*-algebras induced by the left regular representations. These graphs of monoids give rise to some partial group actions and the related transformation groupoids. We give a detailed analysis to closed invariant subspaces and the topological freeness of the partial actions. This enables us to analyze the ideal structure and compute K-theory of the reduced semigroup C*-algebras. As an application, we construct families of pairwise non-conjugate Cartan subalgebras in UCT Kirchberg algebras.

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