Leibniz algebras associated with some finite-dimensional representation of Diamond Lie algebra

Algebra, Analysis and Quantum Probability

Camacho, Luisa M.^1 ; Ladra, Manuel^2 ; Karimjanov, Iqboljon A.^2 ; Omirov, Bakhrom A.^3

Departamento de Matemática Aplicada i, Universidad de Sevilla, Avda. Reina Mercedes, s/n, Sevilla

41012, Spain^1

Department of Algebra, University of Santiago de Compostela, Santiago de Compostela

15782, Spain^2

Institute of Mathematics, National University of Uzbekistan, Dormon Yoli str. 29, Tashkent

100125, Uzbekistan^3

关键词: D-modules;    Finite dimensional;    Leibniz algebras;    Lie Algebra;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/697/1/012006/pdf
DOI  :  10.1088/1742-6596/697/1/012006

来源: IOP

【 摘 要 】

In this paper we classify Leibniz algebras whose associated Lie algebra is four-dimensional Diamond Lie algebra and the ideal generated by squares of elements is represented by one of the finite-dimensional indecomposable D-modules Un1, Un2or Wn1or Wn2.