INVARIANTS OF LIE ALGEBRAS EXTENDED OVER COMMUTATIVE ALGEBRAS WITHOUT UNIT

被引：7

作者：

Zusmanovich, Pasha ^{[1
]}

机构：

[1] Reykjavik Acad, IS-107 Reykjavik, Iceland

来源：

JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS | 2010年 / 17卷

关键词：

Current Lie algebra; Kac-Moody algebras; second cohomology; invariant bilinear form; derivation; LEIBNIZ HOMOLOGY; 2ND COHOMOLOGY; DERIVATIONS;

D O I：

10.1142/S1402925110000817

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We establish results about the second cohomology with coefficients in the trivial module, symmetric invariant bilinear forms, and derivations of a Lie algebra extended over a commutative associative algebra without unit. These results provide a simple unified approach to a number of questions treated earlier in completely separated ways: periodization of semisimple Lie algebras (Anna Larsson), derivation algebras, with prescribed semisimple part, of nilpotent Lie algebras (Benoist), and presentations of affine Kac-Moody algebras.

引用

页码：87 / 102

页数：16

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