Twisted noncommutative equivariant cohomology: Weil and Cartan models

TL;DR

This paper develops Weil and Cartan models for equivariant cohomology in noncommutative spaces with twisted symmetries, extending classical models to noncommutative geometry using Drinfel'd twists.

Contribution

It introduces a framework to incorporate Drinfel'd twisted symmetries into equivariant cohomology models for noncommutative spaces, building on the noncommutative Weil algebra.

Findings

Constructed twisted Weil and Cartan models for noncommutative equivariant cohomology.

Extended classical models to accommodate noncommutative spaces with twisted symmetries.

Demonstrated the implementation of Drinfel'd twists in the models.

Abstract

We propose Weil and Cartan models for the equivariant cohomology of noncommutative spaces which carry a covariant action of Drinfel'd twisted symmetries. The construction is suggested by the noncommutative Weil algebra of Alekseev and Meinrenken; we show that one can implement a Drinfel'd twist of their models in order to take into account the noncommutativity of the spaces we are acting on.