The uniqueness of the decomposition of quadratic Lie algebras

Authors
Zhu, FH Zhu, LS
Citation
Fh. Zhu et Ls. Zhu, The uniqueness of the decomposition of quadratic Lie algebras, COMM ALGEB, 29(11), 2001, pp. 5145-5154
Citations number
12
Categorie Soggetti
Mathematics
Journal title
COMMUNICATIONS IN ALGEBRA
ISSN journal
00927872 → ACNP
Volume
29
Issue
11
Year of publication
2001
Pages
5145 - 5154
Database
ISI
SICI code
0092-7872(2001)29:11<5145:TUOTDO>2.0.ZU;2-V
Abstract
In this paper, we consider the decomposition of a quadratic Lie algebra and the main result is that the decomposition of a quadratic Lie algebra into irreducible nondegenerate ideals is unique up to an isometry (Theorem 3.1). As a corollary, we obtain the uniqueness of the decomposition of an arbitr ary Lie algebra into indecomposable ideals up to an isomorphism (Corollary 3.5.4).