Algebraic quantum kk-theory

TL;DR

This paper develops an algebraic $kk$-theory for $ ext{G}$-module algebras where $ ext{G}$ is an algebraic quantum group, establishing adjointness and duality properties to advance the understanding of equivariant algebraic structures.

Contribution

It introduces an equivariant algebraic $kk$-theory for algebraic quantum groups and explores key properties like adjointness and duality.

Findings

Established an equivariant algebraic $kk$-theory for $ ext{G}$-module algebras.

Proved an adjointness theorem relating smash product and trivial action.

Discussed a duality property within the theory.

Abstract

Let $\mathcal{G}$ be an algebraic quantum group. We introduce an equivariant algebraic $kk$-theory for $\mathcal{G}$-module algebras. We study an adjointness theorem related with smash product and trivial action. We also discuss a duality property.