Biderivations of complete Leibniz algebras
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917024491372544 |
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| author | Di Bartolo, Alfonso Di Fatta, Francesco Paolo La Rosa, Gianmarco |
| author_facet | Di Bartolo, Alfonso Di Fatta, Francesco Paolo La Rosa, Gianmarco |
| contents | If one wishes to define a complete Leibniz algebra in such a way as to extend the notion of a complete Lie algebra, two distinct definitions can be found in the current literature. Since biderivations on complete Lie algebras have already been studied, in order to extend those results and considering that Leibniz algebras are, among others, a natural generalisation of Lie algebras, we study here the biderivations of complete Leibniz algebras according to both definitions. In each case, we provide necessary and sufficient conditions for a bilinear map to be a biderivation of a Leibniz algebra. Finally, we analyse both symmetric and skew-symmetric biderivations, highlighting their structural properties. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_16426 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Biderivations of complete Leibniz algebras Di Bartolo, Alfonso Di Fatta, Francesco Paolo La Rosa, Gianmarco Rings and Algebras Differential Geometry 17A32, 17B05, 17B30, 17B40 If one wishes to define a complete Leibniz algebra in such a way as to extend the notion of a complete Lie algebra, two distinct definitions can be found in the current literature. Since biderivations on complete Lie algebras have already been studied, in order to extend those results and considering that Leibniz algebras are, among others, a natural generalisation of Lie algebras, we study here the biderivations of complete Leibniz algebras according to both definitions. In each case, we provide necessary and sufficient conditions for a bilinear map to be a biderivation of a Leibniz algebra. Finally, we analyse both symmetric and skew-symmetric biderivations, highlighting their structural properties. |
| title | Biderivations of complete Leibniz algebras |
| topic | Rings and Algebras Differential Geometry 17A32, 17B05, 17B30, 17B40 |
| url | https://arxiv.org/abs/2510.16426 |