, Volume 53, Issue 3, pp 321-345

Smash products and outer derivations

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Abstract

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 .

The first author wishes to thank the University of Southern California for its hospitality while this work was being done.
Research of the second author was partially supported by NSF Grant MCS 83-01393.