Article
| Title: | Generalized semidirect sums of Lie algebras and their modules (English) |
| Author: | Lu, Rui |
| Author: | Tan, Youjun |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 75 |
| Issue: | 2 |
| Year: | 2025 |
| Pages: | 699-742 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | Generalized semidirect sums of Lie algebras and their modules are introduced, which are not necessarily (non)-Abelian extensions and may be applied to construct Lie algebras from modules. Some properties of generalized semidirect sums are described. In particular, it is shown that finite dimensional non-solvable Lie algebras can be realized as generalized semidirect sums. The complete classification up to isomorphism of all generalized semidirect sums of $\mathfrak {sl}_2$ and its finite-dimensional irreducible modules is given. (English) |
| Keyword: | Lie algebra |
| Keyword: | module |
| Keyword: | generalized semidirect sum |
| MSC: | 17B05 |
| MSC: | 17B10 |
| DOI: | 10.21136/CMJ.2025.0396-24 |
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| Date available: | 2025-05-20T11:52:04Z |
| Last updated: | 2025-05-26 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152967 |
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