Leibniz algebras associated with representations of filiform Lie algebras

JOURNAL OF GEOMETRY AND PHYSICS

卷:98

Article

Ayupov, Sh. A.¹  Camacho, L. M.²  Khudoyberdiyev, A. Kh.¹  Omirov, B. A.¹ 

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

[2] Univ Seville, Dept Matemat Aplicada 1, E-41012 Seville, Spain

关键词: Filiform algebra;    Heisenberg algebra;    Pock representation;    Minimal faithful representation;   

DOI  :  10.1016/j.geomphys.2015.08.002

来源: Elsevier

【 摘 要 】

In this paper we investigate Leibniz algebras whose quotient Lie algebra is a naturally graded filiform Lie algebra n(n,1). We introduce a Fock module for the algebra n(n,1) and provide classification of Leibniz algebras L whose corresponding Lie algebra L/I is the algebra n(n,1) with condition that the ideal I is a Fock n(n,1)-module, where I is the ideal generated by squares of elements from L. We also consider Leibniz algebras with corresponding Lie algebra n(n,1) and such that the action I x n(n,1) -> I gives rise to a minimal faithful representation of n(n,1). The classification up to isomorphism of such Leibniz algebras is given for the case of n = 4. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

Free