Topologizing Lie algebra cohomology

TL;DR

This paper extends Lie algebra cohomology into a topological framework, demonstrating that key classical results like the Shapiro lemma and van Est isomorphism remain valid in this new setting.

Contribution

It introduces a topological approach to Lie algebra cohomology, generalizing classical theorems to this broader context.

Findings

Classical results are valid in the topological setting

The theory is recast with topological structures

Key isomorphisms are preserved in the new framework

Abstract

We show that the theory of Lie algebra cohomology can be recast in a topological setting and that classical results, such as the Shapiro lemma and the van Est isomorphism, carry over to this augmented context.