Nicolai Stammeier: Aiming for accuracy - boundary quotients of right LCM semigroups revisited

Nicolai Stammeier (Münster) will give a talk with title "Aiming for accuracy - boundary quotients of right LCM semigroups revisited "

Abstract: I will recall the notions of foundation sets and the boundary quotient for right LCM semigroups. This C*-algebra is obtained by modding out products of defect projections over foundation sets in the full semigroup C*-algebra of the right LCM semigroup. Observing that this is in stark contrast to the standard presentations of C*-algebras in the spirit of Cuntz algebras, where a summation relation gets used, we will discuss the possibility of replacing the product relation by a summation relation and arrive at the accurate refinement property. This feature turns out to be quite common among right LCM semigroups. In fact, we are yet to see an example of a right LCM semigroup that has an insufficient supply of accurate foundation sets. Time permitting, we will leave the realm of right LCM semigroups for the sake of finding semigroups without the accurate refinement property.