Super O-operators of Jordan superalgebras and super Jordan Yang-Baxter equations

Abstract

In this paper, the super \mathcal{O}-operators of Jordan superalgebras are introduced and the solutions of super Jordan Yang-Baxter equation are discussed by super \mathcal{O}-operators. Then pre-Jordan superalgebras are studied as the algebraic structure behind the super \mathcal{O}-operators. Moreover, the relations among Jordan superalgebras, pre-Jordan superalgebras, and dendriform superalgebras are established.

Keywords

Super \mathcal{O}-operator / dendriform superalgebra / pre-Jordan superalgebra

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