Infinitesimal deformations of naturally graded filiform Leibniz algebras

JOURNAL OF GEOMETRY AND PHYSICS

卷:86

Article

Khudoyberdiyev, A. Kh.¹  Omirov, B. A.¹ 

[1] Natl Univ Uzbekistan, Inst Math, Tashkent 100125, Uzbekistan

关键词: Leibniz algebra;    The second group of cohomology;    Filiform algebra;    Infinitesimal deformation;    Rigid algebra;   

DOI  :  10.1016/j.geomphys.2014.07.034

来源: Elsevier

【 摘 要 】

In the present paper we describe infinitesimal deformations of complex naturally graded filiform Leibniz algebras. It is known that any n-dimensional filiform Lie algebra can be obtained by a linear integrable deformation of the naturally graded algebra F-n(3)(0). We establish that in the same way any n-dimensional filiform Leibniz algebra can be obtained by an infinitesimal deformation of the filiform Leibniz algebras F-n(1), F-n(2) and F-n(3)(alpha). Moreover, we describe the linear integrable deformations of the above-mentioned algebras with a fixed basis of HL2 in the set of all n-dimensional Leibniz algebras. Among these deformations one new rigid algebra has been found. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

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