ON ONE-DIMENSIONAL LEIBNIZ CENTRAL EXTENSIONS OF A FILIFORM LIE ALGEBRA

被引：21

作者：

Rakhimov, Isamiddin S. ^{[1
,2
]}

Hassan, Munther A. ^{[1
]}

机构：

[1] Univ Putra Malaysia, Inst Math Res INSPEM, Serdang 43400, Selangor Darul, Malaysia

[2] Univ Putra Malaysia, Dept Math, FS, Serdang 43400, Selangor Darul, Malaysia

来源：

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2011年 / 84卷 / 02期

关键词：

Lie algebra; filiform Leibniz algebra; isomorphism; invariant;

D O I：

10.1017/S0004972711002371

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The paper deals with the classification of Leibniz central extensions of a filiform Lie algebra. We choose a basis with respect to which the multiplication table has a simple form. In low-dimensional cases isomorphism classes of the central extensions are given. In the case of parametric families of orbits, invariant functions (orbit functions) are provided.

引用

页码：205 / 224

页数：20

共 50 条

[11] Classification of symmetric Leibniz algebras whose underlying Lie algebra is quasi-filiform
Choriyeva, I. B.
Khudoyberdiyev, A. Kh.
COMMUNICATIONS IN ALGEBRA, 2025,
[12] A cohomological characterization of Leibniz central extensions of Lie algebras
Hu, Naihong
Pei, Yufeng
Liu, Dong
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2008, 136 (02) : 437 - 447
[13] Completable Filiform Lie Algebra
Wu Mingzhong
MECHANICAL AND AEROSPACE ENGINEERING, PTS 1-7, 2012, 110-116 : 183 - 185
[14] Lie symmetry algebra of one-dimensional nonconservative dynamical systems
Liu Cui-Mei
Wu Run-Heng
Fu Jing-Li
CHINESE PHYSICS, 2007, 16 (09): : 2665 - 2670
[15] Leibniz algebra deformations of a Lie algebra
Fialowski, Alice
Mandal, Ashis
JOURNAL OF MATHEMATICAL PHYSICS, 2008, 49 (09)
[16] HOMOLOGY AND CENTRAL EXTENSIONS OF LEIBNIZ AND LIE n-ALGEBRAS
Manuel Casas, Jose
Khmaladze, Emzar
Ladra, Manuel
Van der Linden, Tim
HOMOLOGY HOMOTOPY AND APPLICATIONS, 2011, 13 (01) : 59 - 74
[17] BAND-STRUCTURE OF ONE-DIMENSIONAL QUASICRYSTAL AND LIE-ALGEBRA
OHSAWA, K
NINOMIYA, T
JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 1988, 57 (07) : 2448 - 2455
[18] Bosonic and fermionic representations of Lie algebra central extensions
Lau, M
ADVANCES IN MATHEMATICS, 2005, 194 (02) : 225 - 245
[19] Central extensions of the Lie algebra of symplectic vector fields
Vizman, C
JOURNAL OF LIE THEORY, 2006, 16 (02) : 297 - 309
[20] Derivation Algebra of Quasi R;-filiform Lie Algebra
WU MING-ZHONG (Department of Mathematics
Communications in Mathematical Research, 2012, 28 (03) : 218 - 224

← 1 2 3 4 5 →