Wreath products and Kaluzhnin-Krasner embedding for Lie algebras期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Wreath products and Kaluzhnin-Krasner embedding for Lie algebras

Authors:	V M Petrogradsky Yu P Razmyslov E O Shishkin

Institution:	Faculty of Mathematics, Ulyanovsk State University, Lev Tolstoy 42, Ulyanovsk, 432970 Russia ; Department of Mechanics and Mathematics, Moscow State University, Moscow, 119992 Russia ; Department of Mechanics and Mathematics, Moscow State University, Moscow, 119992 Russia

Abstract:	The wreath product of groups $A\wr B$ is one of basic constructions in group theory. We construct its analogue, a wreath product of Lie algebras. Consider Lie algebras and over a field . Let be the universal enveloping algebra. Then $\bar H=\operatorname{Hom}_K(U(G),H)$ has the natural structure of a Lie algebra, where the multiplication is defined via the comultiplication in . Also, acts by derivations on $\bar H$ via the (left) coregular action. The semidirect sum $\bar H \leftthreetimes G$ we call the wreath product and denote by $H\wr G$ . As a main result, we prove that an arbitrary extension of Lie algebras $0\to H\to L\to G\to 0$ can be embedded into the wreath product $L\hookrightarrow H\wr G$ .

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