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- W4328003395 abstract "Jordan D-bialgebras were introduced by Zhelyabin. In this paper, we use a new approach to study Jordan D-bialgebras by a new notion of the dual representation of the regular representation of a Jordan algebra. Motivated by the essential connection between Lie bialgebras and Manin triples, we give an explicit proof of the equivalence between Jordan D-bialgebras and a class of special Jordan–Manin triples called double constructions of pseudo-euclidean Jordan algebras. We also show that a Jordan D-bialgebra leads to the Jordan Yang–Baxter equation under the coboundary condition and an antisymmetric nondegenerate solution of the Jordan Yang–Baxter equation corresponds to an antisymmetric bilinear form, which we call a Jordan symplectic form on Jordan algebras. Furthermore, there exists a new algebra structure called pre-Jordan algebra on Jordan algebras with a Jordan symplectic form." @default.
- W4328003395 created "2023-03-22" @default.
- W4328003395 creator A5089039474 @default.
- W4328003395 date "2022-03-20" @default.
- W4328003395 modified "2023-09-28" @default.
- W4328003395 title "A New Approach to Jordan D-Bialgebras via Jordan–Manin Triples" @default.
- W4328003395 doi "https://doi.org/10.1142/s100538672300007x" @default.
- W4328003395 hasPublicationYear "2022" @default.
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