Article
Leibniz algebras associated with representations of filiform Lie algebras
Author/s | Ayupov, Sh. A.
Camacho Santana, Luisa María Khudoyberdiyev, Abror Kh. Omirov, Bakhrom Abdazovich |
Department | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) |
Publication Date | 2015 |
Deposit Date | 2019-10-28 |
Published in |
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Abstract | In this paper we investigate Leibniz algebras whose quotient Lie algebra is a naturally graded filiform
Lie algebra nn,1. We introduce a Fock module for the algebra nn,1 and provide classification of Leibniz algebras
L ... In this paper we investigate Leibniz algebras whose quotient Lie algebra is a naturally graded filiform Lie algebra nn,1. We introduce a Fock module for the algebra nn,1 and provide classification of Leibniz algebras L whose corresponding Lie algebra L/I is the algebra nn,1 with condition that the ideal I is a Fock nn,1-module, where I is the ideal generated by squares of elements from L. We also consider Leibniz algebras with corresponding Lie algebra nn,1 and such that the action I × nn,1 ! I gives rise to a minimal faithful representation of nn,1. The classification up to isomorphism of such Leibniz algebras is given for the case of n = 4. |
Project ID. | MTM2013-43687-P |
Citation | Ayupov, S.A., Camacho Santana, L.M., Khudoyberdiyev, A.K. y Omirov, B.A. (2015). Leibniz algebras associated with representations of filiform Lie algebras. Journal of Geometry and Physics, 98 (December 2015), 181-195. |
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