On semi-infinite cohomology of finite dimensional graded algebras

TL;DR

This paper develops a categorical framework for semi-infinite cohomology of finite dimensional graded algebras and applies it to compute cohomology of modules over small quantum groups, extending previous results.

Contribution

It introduces a general categorical setting for semi-infinite cohomology and computes new examples for modules over small quantum groups.

Findings

Categorical interpretation of semi-infinite cohomology.

Computed semi-infinite cohomology for modules over small groups at roots of unity.

Extended Arkhipov's results on semi-infinite cohomology.

Abstract

We describe a general setting for the definition of semi-infinite cohomology of finite dimensional algebras, and provide its categorical interpretation. We apply this interpretation to compute semi-infinite cohomology of some modules over the small group at a root of unity, generalizing an earlier result of S. Arkhipov (conjectured by B. Feigin).