HOMOLOGICAL DIMENSIONS OF INVARIANTS FOR HOPF ALGEBRA ACTIONS

Abstract

Let H be a Hopf algebra acting on a ring A, and let A ^H denote the invariant subring of A. It is shown that if H is semisimple and A is a finitely generated projective right A ^H—module then IdA^H = IdA = Id(A#H). Moreover, if A is a left and right noetherian ring with gl.dimA < infin;, it is deduced that gl.dimA. = gl.dimA.