Article
| Title: | Leibniz algebras arising from symmetric modules and module homomorphisms (English) |
| Author: | Deng, Miting |
| Author: | Lu, Rui |
| Author: | Tan, Youjun |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 76 |
| Issue: | 3 |
| Year: | 2026 |
| Pages: | 1045-1076 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | By introducing a module structure on the tensor product of a symmetric module of a Leibniz algebra, we obtain a construction of Leibniz algebras which generalizes the usual semidirect sums. The resulting Leibniz algebras, called the generalized semidirect sums, are given by a pair of module homomorphisms. Some properties of generalized semidirect sums are described, which are applied to split Leibniz algebras and their symmetric modules. Generalized semidirect sums from the complex 3-dimensional simple Lie algebra and its finite-dimensional irreducible modules are classified up to isomorphism of Leibniz algebras. (English) |
| Keyword: | Leibniz algebra |
| Keyword: | module |
| Keyword: | homomorphism |
| Keyword: | Lie algebra |
| MSC: | 17A32 |
| MSC: | 17B10 |
| DOI: | 10.21136/CMJ.2026.0044-26 |
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| Date available: | 2026-09-11T13:18:09Z |
| Last updated: | 2026-09-14 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/153742 |
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