Semigroup $C^\ast$-algebras and toric varieties

Joachim Cuntz

3:00 pm - 4:00 pm, March 31th, 2017   Science Building A1510

Abstract:

The coordinate ring of a toric variety is the semigroup ring of a finitely generated subsemigroup of Z$^n$. Such semigroups have the interesting feature that their family of constructible ideals is not independent. This is reflected by torsion phenomena in the K-theory of the semigroup $C^\ast$-algebra. We give a complete formula for the K-theory in the case of subsemigroups of Z$^2$.