Leibniz algebras of Heisenberg type

JOURNAL OF ALGEBRA

卷:452

Article

Calderon, A. J.¹  Camacho, L. M.²  Omirov, B. A.³ 

[1] Univ Cadiz, Dept Matemat, Cadiz 11510, Spain

[2] Univ Seville, Dept Matemat Aplicada 1, Avda Reina Mercedes S-N, E-41012 Seville, Spain

[3] Natl Univ Uzbekistan, Inst Math, F Hodjaev Str 29, Tashkent 100125, Uzbekistan

关键词: Heisenberg algebra;    Leibniz algebra;    Fock representation;    Minimal faithful representation;   

DOI  :  10.1016/j.jalgebra.2015.12.018

来源: Elsevier

【 摘 要 】

We introduce and provide a classification theorem for the class of Heisenberg-Fock Leibniz algebras. This type of algebras is formed by those Leibniz algebras L whose corresponding Lie algebras are isomorphic to Heisenberg algebras H-n and whose H-n-modules I, where I denotes the ideal generated by the squares of elements of L, are isomorphic to Back modules. We also consider the three-dimensional Heisenberg algebra H-3 and study three classes of Leibniz algebras with H-3 as corresponding Lie algebra, by taking certain generalizations of the Fock module. Moreover, we describe the class of Leibniz algebras with H-n as corresponding Lie algebra and such that the action I x H-n -> I gives rise to a minimal faithful representation of H-n. The classification of this family of Leibniz algebras for the case of n = 3 is given. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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