Rota-Baxter Operators on pre-Lie superalgebras and beyond
classification
🧮 math.RA
math-phmath.MP
keywords
superalgebraspre-lieoperatorsrota-baxterassociativedendriformbeyondcomplex
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In this paper, we study Rota-Baxter operators and super $\mathcal{O}$-operator of associative superalgebras, Lie superalgebras, pre-Lie superalgebras and $L$-dendriform superalgebras. Then we give some properties of pre-Lie superalgebras constructed from associative superalgebras, Lie superalgebras and $L$-dendriform superalgebras. Moreover, we provide all Rota-Baxter operators of weight zero on complex pre-Lie superalgebras of dimensions $2$ and $3$.
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