Skew-symmetric derivations of a complex Lie algebra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

Skew-symmetric derivations of a complex Lie algebra

Authors:	Ignacio Bajo

Affiliation:	(1) Dept. Matematica Aplicada, E.T.S.I. Industrial, Lagoas-Marcosende, Vigo, Spain

Abstract:	Let be a complex Lie algebra, $mathfrak{G}_0$ its underlying real Lie algebra, a real form of and ·, · the euclidean product induced by the real part of an hermitian inner product on $mathfrak{G}_0$ . Let aut $left( {mathfrak{G}_0 ,leftlangle { cdot , cdot } rightrangle } right)$ be the Lie algebra of skew-symmetric derivations of $mathfrak{G}_0$ . We give necessary and sufficient conditions to ensure that aut $left( {mathfrak{G}_0 ,leftlangle { cdot , cdot } rightrangle } right)$ is composed of skew-hermitian derivations. As an application, we study holomorphy in large subgroups of isometries of Lie groups.

Keywords:	17B40 53C20 53C30
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