Lie triple systems, restricted Lie triple systems, and algebraic groups

JOURNAL OF ALGEBRA

卷:244

Article

Hodge, TL

关键词: Lie triple systems;    algebraic groups;    restricted Lie triple systems;    standard enveloping Lie algebra;    universal enveloping Lie algebra;    representation theory;    involutions;    modular Harish-Chandra modules;   

DOI  :  10.1006/jabr.2001.8890

来源: Elsevier

【 摘 要 】

We define a restricted structure for Lie triple systems in the characteristic p > 2 setting, akin to the restricted structure for Lie algebras, and initiate a study of a theory of restricted modules. In general, Lie triple systems have natural embeddings into certain canonical Lie algebras, the so-called standard and universal embeddings, and any Lie triple system can be shown to arise precisely as the -1-eigenspace of an involution (an automorphism which squares to the identity) on some Lie algebra. We specialize to Lie triple systems which arise as the differentials of involutions on simple, simply connected algebraic groups over algebraically closed fields of characteristic p. Under these hypotheses we completely classify the universal and standard embeddings in terms of the Lie algebra and its universal central extension. (C) 2001 Academic Press.

【 授权许可】

Free