Article
| Title: | Lie $H$-pseudoalgebras with Rota-Baxter $H$-operators (English) |
| Author: | Gai, Botong |
| Author: | Wang, Shuanhong |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 75 |
| Issue: | 4 |
| Year: | 2025 |
| Pages: | 1361-1391 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | A Lie conformal algebra $L$ is defined as a $\mathbb {C}[\partial ]$-module ($\partial $ is an indeterminate), endowed with a $\mathbb {C}$-linear map $L\otimes L\rightarrow \mathbb {C}[\lambda ]\otimes L$, $a\otimes b\rightarrow [a_{\lambda }b]$ satisfying axioms similar to those of Lie algebra. Then Bakalov, D'Andrea and Kac introduced the notion of Lie $H$-pseudoalgebras by replacing the above polynomial algebra $\mathbb {C}[\partial ]$ with any cocommutative Hopf algebra $H$. We first classify solvable Lie $H$-pseudoalgebras of rank two. Then we consider the Rota-Baxter $H$-operators on such Lie $H$-pseudoalgebras. Finally, we study the relationship between Rota-Baxter $H$-operators on Lie $H$-pseudoalgebra and Rota-Baxter operators on its annihilation algebra. (English) |
| Keyword: | Hopf algebra |
| Keyword: | Lie $H$-pseudoalgebra |
| Keyword: | universal enveloping algebra |
| Keyword: | Rota-Baxter $H$-operator |
| Keyword: | annihilation algebra |
| MSC: | 16T05 |
| MSC: | 17B05 |
| MSC: | 17B30 |
| DOI: | 10.21136/CMJ.2025.0169-25 |
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| Date available: | 2025-12-20T07:50:54Z |
| Last updated: | 2025-12-22 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/153248 |
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