Lie Rota-Baxter operators on the Sweedler algebra H4 Full article
| Journal |
International Journal of Algebra and Computation
ISSN: 0218-1967 , E-ISSN: 1793-6500 |
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| Output data | Year: 2024, Volume: 34, Number: 08, Pages: 1159-1189 Pages count : 31 DOI: 10.1142/s0218196724500462 | ||||||||
| Tags | Associative algebra; Lie algebra; Hopf algebra; Rota–Baxter operator. | ||||||||
| Authors |
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| Affiliations |
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Funding (2)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0002 |
| 2 | Russian Science Foundation | 24-21-00102 |
Abstract:
If A is an associative algebra, then we can define the adjoint Lie algebra A(−) and Jordan algebra A(+). It is easy to see that any associative Rota–Baxter (RB) operator on A induces a Lie and Jordan RB operator on A(−) and A(+), respectively. Are there Lie (Jordan) RB operators, which are not associative RB operators? In this paper, we explore these questions for the Sweedler algebra H4, which is a 4-dimensional non-commutative Hopf algebra. More precisely, we describe the RB operators on the adjoint Lie algebra H(−) 4 .
Cite:
Bardakov V.G.
, Nikonov I.M.
, Zhelaybin V.N.
Lie Rota-Baxter operators on the Sweedler algebra H4
International Journal of Algebra and Computation. 2024. V.34. N08. P.1159-1189. DOI: 10.1142/s0218196724500462 WOS Scopus РИНЦ OpenAlex
Lie Rota-Baxter operators on the Sweedler algebra H4
International Journal of Algebra and Computation. 2024. V.34. N08. P.1159-1189. DOI: 10.1142/s0218196724500462 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | May 26, 2024 |
| Accepted: | Sep 2, 2024 |
| Published online: | Oct 28, 2024 |
| Published print: | Jan 15, 2025 |
Identifiers:
| Web of science: | WOS:001347078500001 |
| Scopus: | 2-s2.0-85207903397 |
| Elibrary: | 73823058 |
| OpenAlex: | W4402527420 |
Citing:
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