${\mathbb Z}_n$-equivariant $K$-theory

TL;DR

This paper develops a sequence of cyclic exact sequences to facilitate the computation of the $K$-theory for $C^*$-algebras crossed with finite cyclic groups, specifically ${ m Z}_n$.

Contribution

It introduces a novel sequence of cyclic exact sequences tailored for calculating the $K$-theory of crossed product $C^*$-algebras with cyclic groups.

Findings

Constructed $n-1$ cyclic exact sequences for ${ m Z}_n$-crossed products.

Provides a systematic method for $K$-theory computation in this setting.

Enhances understanding of $K$-theory in equivariant $C^*$-algebra contexts.

Abstract

We construct a sequence of $n-1$ cyclic exact sequences that can be used to compute the $K$-theory of the $C^\star$-algebra crossed product $A \ltimes {\mathbb Z}_n$.