Some cohomologically rigid solvable Leibniz algebras

JOURNAL OF ALGEBRA

卷:560

Article

Camacho, Luisa M.¹  Kaygorodov, Ivan²  Omirov, Bakhrom³  Solijanova, Gulkhayo⁴ 

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

[2] Univ Fed ABC, CMCC, Santo Andre, SP, Brazil

[3] Uzbek Acad Sci, Inst Math, 81 Mirzo Ulugbek St, Tashkent 100041, Uzbekistan

[4] Natl Univ Uzbekistan, 4 Univ St, Tashkent 100174, Uzbekistan

关键词: Lie algebra;    Leibniz algebra;    Nilpotent radical;    Characteristic sequence;    Solvable algebra;    Derivation;   

DOI  :  10.1016/j.jalgebra.2020.05.033

来源: Elsevier

【 摘 要 】

In this paper we describe solvable Leibniz algebras whose quotient algebra by one-dimensional ideal is a Lie algebra with rank equal to the length of the characteristic sequence of its nilpotent radical. We prove that such Leibniz algebra is unique and centerless. Also it is proved that the first and the second cohomology groups of the algebra with coefficients in the adjoint representation is trivial. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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