Smash products and outer derivations
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LetR be a prime ring andL a Lie algebra acting onR as “Q-outer” derivations (if charR=p≠0, assume thatL is restricted). We study ideals and the center of the smash productR #U(L) (respectivelyR #u(L) ifL is restricted) and use these results to study the relationship betweenR and the ring of constantsR L . More generally, for any finite-dimensional Hopf algebraH acting onR such thatR #H satisfies the “ideal intersection property”, we useR #H to study the relationship betweenR and the invariant ringR H .
KeywordsHopf Algebra Left Ideal Prime Ring Polynomial Identity Smash Product
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