B. Burgstaller

activity

20122024

collaborators

5 papers

math.KT2024

On the $K$ -theory in splitexact algebraic $K K$ -theory

Bernhard Burgstaller

It is proven that in the universal splitexact equivariant algebraic $K K$ -theory for algebras, the $K$ -theory groups coincide with classical $K$ -theory in the sense of Phillips. Thi…

math.KT2021

A kind of $K K$ -theory for rings

Bernhard Burgstaller

A group equivariant $K K$ -theory for rings will be defined and studied in analogy to Kasparov's $K K$ -theory for $C^{*}$ -algebras. It is a kind of linearization of the category of ring…

math.KT2019

Aspects of equivariant $K K$ -theory in its generators and relations picture

Bernhard Burgstaller

We give a new proof of the universal property of $K K^{G}$ -theory with respect to stability, homotopy invariance and split-exactness for $G$ a locally compact group, or a locally comp…

math.OA2019

Some remarks in $C^{*}$ - and $K$ -theory

Bernhard Burgstaller

This note consists of three unrelated remarks. First, we demonstrate how roughly speaking $*$ -homomorphisms between matrix stable $C^{*}$ -algebras are exactly the uniformly continuou…

math.KT2012

Equivariant $K K$ -theory of $r$ -discrete groupoids and inverse semigroups

Bernhard Burgstaller

For an $r$ -discrete Hausdorff groupoid $G$ and an inverse semigroup $S$ of slices of $G$ there is an isomorphism between $G$ -equivariant $K K$ -theory and compat…

On the K-theory in splitexact algebraic KK-theory

A kind of KK-theory for rings

Aspects of equivariant KK-theory in its generators and relations picture

Some remarks in C∗- and K-theory

Equivariant KK-theory of r-discrete groupoids and inverse semigroups

On the $K$ -theory in splitexact algebraic $K K$ -theory

A kind of $K K$ -theory for rings

Aspects of equivariant $K K$ -theory in its generators and relations picture

Some remarks in $C^{*}$ - and $K$ -theory

Equivariant $K K$ -theory of $r$ -discrete groupoids and inverse semigroups