Cuntz Semigroups of Compact-Type Hopf C*-Algebras

The Cuntz Semigroup of Continuous Functions into Certain Simple C∗-algebras

This paper contains computations of the Cuntz semigroup of separable C∗-algebras of the form C0(X, A), where A is a unital, simple, Z-stable ASH algebra. The computations describe the Cuntz semigroup in terms of Murray-von Neumann semigroups of C(K, A) for compact subsets K of X. In particular, the computation shows that the Elliott invariant is functorially equivalent to the invariant given by...

Actions of Semigroups on Directed Graphs and Their C∗-algebras

A free action α of a group G on a row-finite directed graph E induces an action α∗ on its Cuntz-Krieger C ∗-algebra C∗(E), and a recent theorem of Kumjian and Pask says that the crossed product C∗(E) ×α∗ G is stably isomorphic to the C∗-algebra C∗(E/G) of the quotient graph. We prove an analogue for free actions of Ore semigroups. The main ingredients are a new generalisation of a theorem of Gr...

On a groupoid construction for actions of certain inverse semigroups

We consider a version of the notion of F -inverse semigroup (studied in the algebraic theory of inverse semigroups). We point out that an action of such an inverse semigroup on a locally compact space has associated a natural groupoid construction, very similar to the one of a transformation group. We discuss examples related to Toeplitz algebras on subsemigroups of discrete groups, to Cuntz-Kr...

Reiter’s Properties for the Actions of Locally Compact Quantum Goups on von Neumann Algebras

Semigroup C*-algebras and Amenability of Semigroups

We construct reduced and full semigroup C*-algebras for left cancellative semigroups. Our new construction covers particular cases already considered by A. Nica and also Toeplitz algebras attached to rings of integers in number fields due to J. Cuntz. Moreover, we show how (left) amenability of semigroups can be expressed in terms of these semigroup C*-algebras in analogy to the group case.