Title: Toeplitz algebras and boundary quotients for submonoids of groups
Abstract: We define a universal Toeplitz C*-algebra Tu(P) and use it to study the reduced Toeplitz C*-algebra Tr(P) when P is a submonoid of a group. We start by proving faithfulness and uniqueness results that generalize classical results of Coburn, Douglas, and Cuntz, and we then focus on a universal boundary quotient ∂Tu(P), which allows us to give straightforward conditions on P for the reduced boundary quotient ∂Tλ(P) to be purely infinite simple. As applications, we consider non-maximal orders in number fields and right LCM monoids with nontrivial units.
This is joint work with Camila F. Sehnem.