Work

Anticenter-Symmetric Bialgebras

Year: 2025

Type: article

Abstract: This paper develops a bialgebra theory for anticenter-symmetric algebras by introducing the concept of an anticenter-symmetric bialgebra, equivalent to a Manin triple of anticenter-symmetric algebras. A study of this framework leads to the anticenter-symmetric Yang-Baxter equation in anticenter-symmetric algebras, analogous to the classical Yang-Baxter equation in Mock Lie algebras and the associative Yang-Baxter equation.An unexpected finding is that the anticenter-symmetric and associative Yang-Baxter equations share the same form. Additionally, skew-symmetric solutions to the anticenter-symmetric Yang-Baxter equation define anticenter-symmetric bialgebras. To advance the theory, the paper introduces O-operators and pre-anticentersymmetric algebras, which facilitate the construction of these solutions and provide a foundation for further exploration.

Source: Asian Research Journal of Mathematics

DOI: 10.9734/arjom/2025/v21i5926

Authors: Gbevewou Damien Houndedji, Cyrille Essossolim Haliya

Institutions: Gamal Abdel Nasser University of Conakry, Université d'Abomey-Calavi

Language: English

Topic: Advanced Topics in Algebra

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4409828453

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