Original Articles

HOMOLOGICAL DIMENSIONS OF INVARIANTS FOR HOPF ALGEBRA ACTIONS

Published in: Quaestiones Mathematicae
Volume 22 , issue 2 , 1999 , pages: 183–186

DOI: 10.1080/16073606.1999.9632072

Author(s): Zhixi Wang Department of Mathematics, China , Shilin Yang Computer Institute, China

Keywords: 16E10 , 16S40 , 16W30 , 16W50 , 16E10 , 16S40 , 16W30 , 16W50

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.

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