C* vs. coarse properties of inverse semigroups

Diego Martinez (University Carlos III de Madrid - ICMAT)

Thursday 21st October 16:00-17:00 Maths 311B/Online

Abstract

Inverse semigroups are a generalization of groups, where elements in an inverse semigroup can be thought of as partial symmetries of a space (instead of global symmetries, as in the group case). Out of these one can construct a uniform Roe algebra algebra just
as in the group case, and study its properties. In this talk, we will study some coarse properties of the inverse semigroup and relate them to C* properties of its associated C*-algebras. For instance, one can study amenability of the semigroup, and relate
the trace space of the uniform Roe algebra with certain invariant measures. Likewise, we shall characterize when such C*-algebra is nuclear by means of the semigroup having property A. Time permitting, we will also talk about properties that guarantee when
the reduced semigroup C*-algebra is quasi-diagonal. This talk is based on joint work with Pere Ara and Fernando Lledó.

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