On smash products of transitive module algebras

Abstract

Let H be a semisimple Hopf algebra over a field of characteristic 0, and A a finite-dimensional transitive H-module algebra with a 1-dimensional ideal. It is proved that the smash product A#H is isomorphic to a full matrix algebra over some right coideal subalgebra N of H. The correspondence between A and such N and the special case A = k(X) of function algebra on a finite set X are considered.

Keywords

Semisimple Hopf algebra / Smash product / Transitive module algebra

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