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Journal of Lie Theory 12 (2002), No. 2, 369--395
Copyright Heldermann Verlag 2002

Polynomial Identities in Smash Products

Yuri Bahturin
Dept. of Mathematics and Statistics, Memorial University, St. John's, NF A1C 5S7, Canada

Victor M. Petrogradsky
Faculty of Mathematics, Ulyanovsk State University, Lev Tolstoy 42, 432700 Ulyanovsk, Russia

Suppose that a group G acts by aumorphisms on a (restricted) Lie algebra L over a field K of positive characteristic. This gives rise to smash products U(L) # K[G] and u(L)# K[G]. We find necessary and sufficient conditions for these smash products to satisfy a nontrivial polynomial identity.

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