Equivariant algebraic kk-theory and adjointness theorems

TL;DR

This paper develops an equivariant algebraic kk-theory framework for G-algebras and G-graded algebras, establishing adjointness theorems and an algebraic Green-Julg Theorem to facilitate computations.

Contribution

It introduces an equivariant algebraic kk-theory and proves new adjointness theorems, including an algebraic Green-Julg Theorem, advancing the theoretical foundation and computational tools in the field.

Findings

Established an equivariant algebraic kk-theory for G-algebras and G-graded algebras.

Proved adjointness theorems related to crossed product, induction, and restriction.

Derived an algebraic Green-Julg Theorem for computational applications.

Abstract

We introduce an equivariant algebraic kk-theory for G-algebras and G-graded algebras. We study some adjointness theorems related with crossed product, trivial action, induction and restriction. In particular we obtain an algebraic version of the Green-Julg Theorem which gives us a computational tool.