Complex cyclic Leibniz superalgebras

Since Loday introduction of Leibniz algebras as a generalisation of Lie algebras, many results of the theory of Lie algebras have been extended to Leibniz algebras. Cyclic Leibniz algebras, which are generated by one element, have no equivalent into Lie algebras, though. This fact provides cyclic Le...

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Detalles Bibliográficos
Autores: Camacho Santana, Luisa María, Navarro, R. M., Omirov, Bakhrom Abdazovich
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:11441/114982
Acceso en línea:https://hdl.handle.net/11441/114982
https://doi.org/10.1007/s13163-020-00370-y
Access Level:acceso abierto
Palabra clave:Leibniz superalgebra
Cyclic Leibniz superalgebra
Null-filiform superalgebra
Infinitesimal deformation
Irreducible component
Descripción
Sumario:Since Loday introduction of Leibniz algebras as a generalisation of Lie algebras, many results of the theory of Lie algebras have been extended to Leibniz algebras. Cyclic Leibniz algebras, which are generated by one element, have no equivalent into Lie algebras, though. This fact provides cyclic Leibniz algebras with important properties. Throughout the present paper we extend the concept of cyclic to Leibniz superalgebras, obtaining then the definition, as long as the description and classification of finite-dimensional complex cyclic Leibniz superalgebras. Furthermore, we prove that any cyclic Leibniz superalgebra can be obtained by means of infinitesimal deformations of the null-filiform Leibniz superalgebra. We also obtain a description of irreducible components in the variety of Leibniz algebras and superalgebras.