Boundary Quotients of Semigroup C*-algebras
Charles Starling (University of Ottawa)
Tuesday 2nd August, 2016 16:00-17:00 Maths 522
The construction due to Li of a C*-algebra associated to a left-cancellative semigroup P generalizes many interesting classes of C*-algebras. These algebras are akin to Toeplitz algebras, and in this analogy their boundary quotients play the role of the Cuntz algebras. Li's recent work on these algebras focuses on the case where P embeds in a group. The class of semigroups which embed into groups is a large and rich class, though it does not include a great many interesting examples -- for instance semigroups obtained from self-similar groups. In this talk we discuss the boundary quotients of the C*-algebras of such P by using a canonical embedding into an inverse semigroup, and find algebraic conditions on P which guarantee that the boundary quotient is simple and purely infinite.