Some cohomologically rigid solvable Leibniz algebras

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 an...

Descripción completa

Detalles Bibliográficos
Autores: Camacho Santana, Luisa María, Kaygorodov, Ivan, Omirov, Bakhrom Abdazovich, Solijanova, Gulkhayo
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2020
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/115106
Acceso en línea:https://hdl.handle.net/11441/115106
https://doi.org/10.1016/j.jalgebra.2020.05.033
Access Level:acceso abierto
Palabra clave:Lie algebras
Leibniz algebra
Nilpotent radical
Characteristic sequence
Solvable algebra
Derivations
2-Cocycle
Rigid algebra
Descripción
Sumario: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.