$ω$-Lie bialgebras and $ω$-Yang-Baxter equation
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909836480872448 |
|---|---|
| author | Sun, Yining Hao, Zeyu Zhang, Ziyi Chen, Liangyun |
| author_facet | Sun, Yining Hao, Zeyu Zhang, Ziyi Chen, Liangyun |
| contents | In this paper, we introduce the definition of multiplicative $ω$-Lie bialgebra, which is equivalent to the Manin triples and matched pairs. We also study the $ω$-Yang-Baxter equation and Yang-Baxter $ω$-Lie bialgebra. The skew-symmetric solutions of the $ω$-Yang-Baxter equation can be used to construct Yang-Baxter $ω$-Lie bialgebra. We further introduce the concept of the $ω$-$\mathcal{O}$-operator, which can be constructed from a left-symmetric algebras, and based on the $ω$-$\mathcal{O}$-operator, we construct skew-symmetric solutions to the $ω$-Yang--Baxter equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_09630 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $ω$-Lie bialgebras and $ω$-Yang-Baxter equation Sun, Yining Hao, Zeyu Zhang, Ziyi Chen, Liangyun Rings and Algebras In this paper, we introduce the definition of multiplicative $ω$-Lie bialgebra, which is equivalent to the Manin triples and matched pairs. We also study the $ω$-Yang-Baxter equation and Yang-Baxter $ω$-Lie bialgebra. The skew-symmetric solutions of the $ω$-Yang-Baxter equation can be used to construct Yang-Baxter $ω$-Lie bialgebra. We further introduce the concept of the $ω$-$\mathcal{O}$-operator, which can be constructed from a left-symmetric algebras, and based on the $ω$-$\mathcal{O}$-operator, we construct skew-symmetric solutions to the $ω$-Yang--Baxter equation. |
| title | $ω$-Lie bialgebras and $ω$-Yang-Baxter equation |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2510.09630 |