Zinbiel superalgebras
Throughout the present work, we extend the study of Zinbiel algebras to Zinbiel superalgebras. In particular, we show that all Zinbiel superalgebras over an arbitrary field are nilpotent in the same way as occurs for Zinbiel algebras. In addition, and since the most important cases of nilpotent alge...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/156621 |
| Acceso en línea: | https://hdl.handle.net/11441/156621 |
| Access Level: | acceso abierto |
| Palabra clave: | Zinbiel superalgebra Dual Leibniz superalgebra Nilpotent superalgebra Algebraic classification |
| Sumario: | Throughout the present work, we extend the study of Zinbiel algebras to Zinbiel superalgebras. In particular, we show that all Zinbiel superalgebras over an arbitrary field are nilpotent in the same way as occurs for Zinbiel algebras. In addition, and since the most important cases of nilpotent algebras or superalgebras are those with maximal nilpotency index, we study the complex null-filiform Zinbiel superalgebra proving that it is unique up to isomorphism. After that, we characterize the naturally graded filiform ones and obtain low-dimensional classifications. |
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