Witherspoon, Sarah2012-10-192012-10-222017-04-072012-10-192012-10-222017-04-072012-082012-10-19http://hdl.handle.net/1969.1/ETD-TAMU-2012-08-11589In 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.en-USCohomologyThesis