On naturally graded Lie and Leibniz superalgebras
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909081056313344 |
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| author | Camacho, Luisa Navarro, Rosa M. Sánchez, J. M. |
| author_facet | Camacho, Luisa Navarro, Rosa M. Sánchez, J. M. |
| contents | In general, the study of gradations has always represented a cornerstone in algebra theory. In particular, \textit{naturally graded} seems to be the first and the most relevant gradation when it comes to nilpotent algebras, a large class of solvable ones. In fact, many families of relevant solvable algebras have been obtained by extensions of naturally graded nilpotent algebras, i.e. solvable algebras with a well-structured nilradical. Thus, the aim of this work is introducing the concept of naturally graded for superalgebra structures such as Lie and (non-Lie) Leibniz. After having defined naturally graded Lie and Leibniz superalgebras, we characterize natural gradations on a very important class of each of them, that is, those with maximal super-nilindex. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_13016 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On naturally graded Lie and Leibniz superalgebras Camacho, Luisa Navarro, Rosa M. Sánchez, J. M. Rings and Algebras In general, the study of gradations has always represented a cornerstone in algebra theory. In particular, \textit{naturally graded} seems to be the first and the most relevant gradation when it comes to nilpotent algebras, a large class of solvable ones. In fact, many families of relevant solvable algebras have been obtained by extensions of naturally graded nilpotent algebras, i.e. solvable algebras with a well-structured nilradical. Thus, the aim of this work is introducing the concept of naturally graded for superalgebra structures such as Lie and (non-Lie) Leibniz. After having defined naturally graded Lie and Leibniz superalgebras, we characterize natural gradations on a very important class of each of them, that is, those with maximal super-nilindex. |
| title | On naturally graded Lie and Leibniz superalgebras |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2401.13016 |