Wreath Products and Kaluzhnin-krasner Embedding for Lie Algebras
نویسنده
چکیده
The wreath product of groups A B is one of basic constructions in group theory. We construct its analogue, a wreath product of Lie algebras. Consider Lie algebras H and G over a field K. Let U(G) be the universal enveloping algebra. Then H̄ = HomK(U(G), H) has the natural structure of a Lie algebra, where the multiplication is defined via the comultiplication in U(G). Also, G acts by derivations on H̄ via the (left) coregular action. The semidirect sum H̄ G we call the wreath product and denote by H G. As a main result, we prove that an arbitrary extension of Lie algebras 0 → H → L → G → 0 can be embedded into the wreath product L ↪→ H G.
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