Year: 2025
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Sun, Yining, Hao, Zeyu, Zhang, Ziyi, Chen, Liangyun
Language: English
Topic: Advanced Topics in Algebra
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7091187882
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