Work

Extending structures for pre-Poisson algebras and pre-Poisson bialgebras

Year: 2025

Type: preprint

Abstract: In this paper, we explore the extending structures problem by the unified product for pre-Poisson algebras. In particular, the crossed product and the factorization problem are investigated. Furthermore, a special case of extending structures is studied under the case of pre-Poisson algebras, which leads to the discussion of bicrossed products and matched pairs of pre-Poisson algebras. We develop a bialgebra theory for pre-Poisson algebras and establish the equivalence between matched pairs and pre-Poisson bialgebras. We study coboundary pre-Poisson bialgebras, which lead to the introduction of the pre-Poisson Yang-Baxter equation (PPYBE). A symmetric solution of the PPYBE naturally gives a coboundary pre-Poisson bialgebra.

Source: arXiv (Cornell University)

Authors: Zhu, Qianwen, Liu, Guilai, Sun, Qinxiu

Institutions: Zhejiang University of Science and Technology, Nankai University

Language: English

Topic: Advanced Topics in Algebra

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Natural Science Foundation of Zhejiang Province

Award: 共形代数的范畴化研究

OpenAlex ID: W6979330874

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