Finite Generation of the Cohomology of Quotients of PBW Algebras

TL;DR

This paper proves that the cohomology of quotients of PBW algebras is finitely generated by relating it to quantum symmetric algebra cohomology, using spectral sequences and a finite generation lemma.

Contribution

It establishes finite generation of cohomology for quotients of PBW algebras by connecting them to quantum symmetric algebra cohomology, extending previous results.

Findings

Cohomology of quotients of PBW algebras is finitely generated.

Uses spectral sequence and finite generation lemma techniques.

Provides a method to relate PBW algebra cohomology to quantum symmetric algebra cohomology.

Abstract

In this article we prove finite generation of the cohomology of quotients of a PBW algebra A by relating it to the cohomology of quotients of a quantum symmetric algebra S which is isomorphic to the associated graded algebra of A. The proof uses a spectral sequence argument and a finite generation lemma adapted from Friedlander and Suslin.