Extending structures for pre-Poisson algebras and pre-Poisson bialgebras
Rings and Algebras
2025-04-22 v1
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.
Keywords
Cite
@article{arxiv.2504.15092,
title = {Extending structures for pre-Poisson algebras and pre-Poisson bialgebras},
author = {Qianwen Zhu and Guilai Liu and Qinxiu Sun},
journal= {arXiv preprint arXiv:2504.15092},
year = {2025}
}