2021/03/02 by Jiawen Shan, Runxuan Zhang, Shan, Jiawen +1
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2103.02064
openalex publication_date 2021/03/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate connections between \mathcal O-operators of Poisson superalgebras and skew-symmetric solutions of the Poisson Yang-Baxter equation (PYBE). We prove that a skew-symmetric solution of the PYBE on a Poisson superalgebra can be interpreted as an \mathcal O-operator associated to the co-regular representation. We show that this connection can be enhanced with symplectic forms when considering non-degenerate skew-symmetric solutions. We also show that \mathcal O-operators associated to a general representation could give skew-symmetric solutions of the PYBE in certain semi-direct product of Poisson superalgebras.