Infinitesimal deformations of the lie superalgebra Ln,m

被引：16

作者：

Gomez, J. R. ^{[2
]}

Khakimdjanov, Yu. ^{[3
]}

Navarro, R. M. ^{[1
]}

机构：

[1] Univ Extremadura, Dept Matemat, Caceres, Spain

[2] Univ Seville, Dpto Matemat Aplicada 1, Seville, Spain

[3] Univ Haute Alsace, Lab Math & Applicat, Mulhouse, France

来源：

JOURNAL OF GEOMETRY AND PHYSICS | 2008年 / 58卷 / 07期

关键词：

Lie superalgebras; cohomology; deformation; nilpotent; filiform;

D O I：

10.1016/j.geomphys.2008.02.005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we continue the study of the infinitesimal deformations of the Lie superalgebra L-n,L-m that we have started in [M. Bordemann, J.R. Gomez, Yu. Khakimdjanov, R.M. Navarro, Some deformations of nilpotent Lie superalgebras, J. Geom. Phys. 57 (2007) 1391-1403]. These deformations allow us to obtain all filiform Lie superalgebras. In [M. Bordemann, J.R. Gomez, Yu. Khakimdjanov, R.M. Navarro, Some deformations of nilpotent Lie superalgebras, J. Geom. Phys. 57 (2007) 1391-1403], we gave a method that allows us to determine the dimension of the space of deformations of type Hom(S-2(L-1(n,m)).L-0(n,m)) and we calculated a basis of the aforementioned space of deformations for n >= 2m - 1. In this paper, we conclude the study by developing a method to calculate a basis of the space of deformations Hom(S-2(L-1(n,m)).L-0(n,m)) for the rest of possibilities n < 2m - 1. We particularize for even n and also give an algorithm for computing a cocycle basis for the given concrete dimensions n and in. (C) 2008 Elsevier B.V. All rights reserved.

引用

页码：849 / 859

页数：11

共 10 条

[1] Some deformations of nilpotent Lie superalgebras [J].