Imbedding Of Lie Triple Systems Into Lie Algebras

Journal of Algebra（2011）

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摘要

We show that the category of Lie triple systems is equivalent to a full subcategory of the category of Z(2)-graded Lie algebras and give two intrinsic characterizations of this subcategory. As a corollary we obtain an analogous result for imbedding of symmetric spaces into Lie groups with involutions. (C) 2011 Elsevier Inc. All rights reserved.

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关键词

Graded Lie algebra,Lie triple system,Universal central extension,Category equivalence,Lie group with involution,Symmetric space

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