2023/09/09 by Chengming Bai, Li Guo, Bai, Chengming +3
Computer Science · Mathematics · #16T23 #17B10 #17B38 #17B60 #17B80 #17B81 #81R05 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Matrix Theory and Algorithms #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.2309.04808
openalex publication_date 2023/09/09 · openalex created_date 2023/09/14 · openalex updated_date 2026/07/28
This paper studies super r-matrices and operator forms of the super classical Yang-Baxter equation. First by a unified treatment, the classical correspondence between r-matrices and O-operators is generalized to a correspondence between homogeneous super r-matrices and homogeneous O-operators. Next, by a parity reverse of Lie superalgebra representations, a duality is established between the even and the odd O-operators, giving rise to a parity duality among the induced super r-matrices. Thus any homogeneous \OO-operator or any homogeneous super r-matrix with certain supersymmetry produces a parity pair of super r-matrices, and generates an infinite tree hierarchy of homogeneous super r-matrices. Finally, a pre-Lie superalgebra naturally defines a parity pair of O-operators, and thus a parity pair of super r-matrices.