On The Finite Generation Of Relative Cohomology For Lie Superalgebras

TL;DR

This paper proves that the relative cohomology ring of classical Lie superalgebras is finitely generated, constructs a spectral sequence for Cohen-Macaulay conditions, and defines support varieties for modules, extending previous work.

Contribution

It establishes finite generation of relative cohomology rings for classical Lie superalgebras and introduces support varieties based on this cohomology.

Findings

Finite generation of the cohomology ring is proven.

A spectral sequence is constructed to analyze Cohen-Macaulay properties.

Support varieties for modules are defined and generalized.

Abstract

The author establishes finite-generation of the cohomology ring of a classical Lie superalgebra relative to an even subsuperalgebra. A spectral sequence is constructed to provide conditions for when this relative cohomology ring is Cohen-Macaulay. With finite generation established, support varieties for modules are defined via the relative cohomology, which generalize those of [BKN-1]