Hopf代数作用中轨道与稳定化子的结构

On Actions of Finite-Dimensional Hopf Algebras of Algebras:Orbits and Stabilizers

设H是一个有限维的Hopf代数,A是有限维的左H-模代数,I是A的任一极小H-理想.任取A的极小理想I1■I,用维数公式证明了轨道模代数OA(I1)≌I.还考虑了当AH■A是右H*-Galois扩张时,稳定化子StabA(V)的结构,其中V是左A-模.

Let H be a finite-dimensional Hopf algebra, and A a semisimple left H-module algebra .For any minimal H-ideal I∈A, choose a minimal ideal of A such that I1∈I.It is proved that the orbit module al-gebra OA （I1） is isomorphic to I by means of dimension equation .The structure of the stabilizer StabA （V） is also considered in the case of AH ∈ A being right H＊-Galois extension, where V is a left A-module.