Quasitriangular and factorizable Poisson bialgebras

Yuanchang Lin and Dilei Lu

Vol. 343 (2026), No. 2, 453–483

DOI: 10.2140/pjm.2026.343.453

Abstract

We introduce the notions of quasitriangular and factorizable Poisson bialgebras. A factorizable Poisson bialgebra induces a factorization of the underlying Poisson algebra. We prove that the Drinfeld classical double of a Poisson bialgebra naturally admits a factorizable Poisson bialgebra structure. Furthermore, we introduce the notion of quadratic Rota–Baxter Poisson algebras and show that a quadratic Rota–Baxter Poisson algebra of zero weight induces a triangular Poisson bialgebra. Moreover, we establish a one-to-one correspondence between factorizable Poisson bialgebras and quadratic Rota–Baxter Poisson algebras of nonzero weights. Finally, we establish the quasitriangular and factorizable theories for differential antisymmetric infinitesimal (ASI) bialgebras, and construct quasitriangular and factorizable Poisson bialgebras from quasitriangular and factorizable (commutative and cocommutative) differential ASI bialgebras respectively.

Keywords

Poisson algebra, Poisson Yang–Baxter equation, quasitriangular Poisson bialgebra, factorizable Poisson bialgebra, quadratic Rota–Baxter Poisson algebra, differential antisymmetric infinitesimal bialgebra

Mathematical Subject Classification

Primary: 16S32, 16T10, 17A30, 17B62, 17B63

Secondary: 17B38, 81R60

Milestones

Received: 7 October 2025

Revised: 20 February 2026

Accepted: 13 April 2026

Published: 22 May 2026