Hannes Thiel

Tensor products and regularity properties of Cuntz semigroups

The Cuntz semigroup of a C*-algebra is an important invariant in the structure and classification theory of C*-algebras. It captures more information than K-theory but is often more delicate to handle. We systematically study the lattice and category theoretic aspects of Cuntz semigroups. Given a C*-algebra

A characterization of semiprojectivity for commutative C*-algebras

A

Banach algebras generated by an invertible isometry of an Lp-space

, its (concrete) Cuntz semigroup

Quotients of Banach algebras acting on Lp-spaces

Cu(A)

Semiprojectivity with and without a group action

is an object in the category

Group Algebras Acting on \(L^p\)-Spaces

Cu

The Topological Dimension of Type I C ∗ -Algebras

of (abstract) Cuntz semigroups, as introduced by Coward, Elliott and Ivanescu. To clarify the distinction between concrete and abstract Cuntz semigroups, we will call the latter

Representations of

Cu

p

-semigroups. We establish the existence of tensor products in the category

-convolution algebras on

Cu