ω-Lie bialgebras and ω-Yang-Baxter equation

2025/09/28 by Sun, Yining, Hao, Zeyu, Zhang, Ziyi +1
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2510.09630

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-O-operator, which can be constructed from a left-symmetric algebras, and based on the ω-O-operator, we construct skew-symmetric solutions to the ω-Yang--Baxter equation.

Citations

• Biderivations, local and 2-local derivation and automorphism of simple ω-Lie algebras
• Nearly associative and nearly Hom-associative algebras and bialgebras
• The classical Hom-Yang-Baxter equation and Hom-Lie bialgebras
• On the Associative Analog of Lie Bialgebras
• Generalized Derivations of Lie Algebras

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• Mock-Lie bialgebras and mock-Lie analogue of the classical Yang-Baxter equation
• Lie algebras and Yang-Baxter equations
• Rota-Baxter Lie bialgebras, classical Yang-Baxter equations and special L-dendriform bialgebras
• Yang-Baxter operators from algebra structures and Lie superalgebras
• The classical Hom-Yang-Baxter equation and Hom-Lie bialgebras