Minimal representations of filiform Lie algebras and their application for construction of Leibniz algebras

JOURNAL OF GEOMETRY AND PHYSICS

卷:144

Article

Karimjanov, I. A.¹  Ladra, M.¹ 

[1] Univ Santiago de Compostela, Dept Matemat, Santiago De Compostela 15782, Spain

关键词: Lie algebra;    Leibniz algebra;    Filiform algebra;    Minimal faithful representation;   

DOI  :  10.1016/j.geomphys.2019.06.009

来源: Elsevier

【 摘 要 】

In this paper we find minimal faithful representations of several classes of filiform Lie algebras by means of strictly upper-triangular matrices. We investigate Leibniz algebras whose corresponding Lie algebras L/I are filiform Lie algebras such that the action I x L/I -> I gives rise to a minimal faithful representation of a filiform Lie algebra, where I is the ideal generated by the squares of the elements of the algebra L. The classification up to isomorphism of such Leibniz algebras is given for low-dimensional cases. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free