Finite Generation of Cohomology of Quotients of PBW Algebras

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