Conjugacy of Cartan subalgebras of complex finite-dimensional Leibniz algebras

被引：43

作者：

Omirov, B. A. ^{[1
]}

机构：

[1] Uzbek Acad Sci, Inst Math, Tashkent 700143, Uzbekistan

来源：

JOURNAL OF ALGEBRA | 2006年 / 302卷 / 02期

关键词：

Cartan subalgebra; regular element; Lie algebra; Leibniz algebra;

D O I：

10.1016/j.jalgebra.2006.01.004

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In the present work the properties of Cartan subalgebras and their connection with regular elements in finite-dimensional Lie algebras are extended to the case of Leibniz algebras. It is shown that Cartan subalgebras and regular elements of a Leibniz algebra correspond to Cartan subalgebras and regular elements of a Lie algebra by a natural homomorphism. Conjugacy of Cartan subalgebras of Leibniz algebras is shown. (c) 2006 Elsevier Inc. All rights reserved.

引用

页码：887 / 896

页数：10

共 11 条

[1] On nilpotent and simple Leibniz algebras [J].

Albeverio, S ;

Ayupov, SA ;

Omirov, BA .

COMMUNICATIONS IN ALGEBRA, 2005, 33 (01) :159-172

[2]

ALBEVERIO S, 2004, CARTAN SUBALGEBRAS C

[3]

Ayupov SA, 1998, ALGEBRA AND OPERATOR THEORY, P1

[4] On some classes of nilpotent Leibniz algebras [J].

Ayupov, SA ;

Omirov, BA .

SIBERIAN MATHEMATICAL JOURNAL, 2001, 42 (01) :15-24

[5] Homology and cohomology with coefficients, of an algebra over a quadratic operad [J].

Balavoine, D .

JOURNAL OF PURE AND APPLIED ALGEBRA, 1998, 132 (03) :221-258

[6] Ten-term exact sequence of Leibniz homology [J].

Casas, JM ;

Pirashvili, T .

JOURNAL OF ALGEBRA, 2000, 231 (01) :258-264

[7] Crossed extensions of Leibniz algebras [J].

Casas, JM .

COMMUNICATIONS IN ALGEBRA, 1999, 27 (12) :6253-6272

[8] Leibniz homology of dialgebras of matrices [J].

Frabetti, A .

JOURNAL OF PURE AND APPLIED ALGEBRA, 1998, 129 (02) :123-141

[9] The second Leibniz homology group for Kac-Moody Lie algebras [J].

Gao, Y .

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2000, 32 :25-33

[10]

JACOBSON N, 1962, LIE ALBEBRAS

← 1 2 →