Leibniz algebras in which all centralisers of nonzero elements are zero algebras
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913245378379776 |
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| author | Towers, David A. |
| author_facet | Towers, David A. |
| contents | This paper is concerned with generalising the results for Lie $CT$-algebras to Leibniz algebras. In some cases our results give a generalisation even for the case of a Lie algebra. Results on $A$-algebras are used to show every Leibniz $CT$-algebra over an algebraically closed field of characteristic different from 2,3 is solvable or is isomorphic to $sl_2(F)$. A characterisation is then given for solvable Leibniz $CT$-algebras. It is also shown that the class of solvable Leibniz $CT$-algebras is factor closed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_17331 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Leibniz algebras in which all centralisers of nonzero elements are zero algebras Towers, David A. Rings and Algebras Group Theory 17A32, 17B05, 17B20, 17B30, 17B50 This paper is concerned with generalising the results for Lie $CT$-algebras to Leibniz algebras. In some cases our results give a generalisation even for the case of a Lie algebra. Results on $A$-algebras are used to show every Leibniz $CT$-algebra over an algebraically closed field of characteristic different from 2,3 is solvable or is isomorphic to $sl_2(F)$. A characterisation is then given for solvable Leibniz $CT$-algebras. It is also shown that the class of solvable Leibniz $CT$-algebras is factor closed. |
| title | Leibniz algebras in which all centralisers of nonzero elements are zero algebras |
| topic | Rings and Algebras Group Theory 17A32, 17B05, 17B20, 17B30, 17B50 |
| url | https://arxiv.org/abs/2402.17331 |