Rota-Baxter Operations Of Low Dimensional Twisted Heisenberg Lie Superalgebras

The research of twisted Heisenberg Lie superalgebras plays an important role in the field of solvable Lie superalgebras.Rota-Baxter operators have important applications in splitting of algebras,combinatorial study of rooted trees noncommutative analogue of Poisson geometry and so on.Recently,the study for Rota-Baxter operator of low-dimensional algebras has become one of the important research topic.More and more scholars devote themselves to the research field of Rota-Baxter operator.In the Lie algebras and Lie superalgebras,the weighted zero Rota-Baxter operators are the solutions of Yang-Baxter equations.In this paper,the Rota-Baxter operators of low-dimensional twisted Heisenberg Lie superalgebras are studied.Firstly,the concept of Rota-Baxter operators with weighted zero and one in the Lie superalgebras.We calculate the Rota-Baxter operators for weighted zero and one of 3-dimensional even and odd twisted Heisenberg Lie superalgebras.Next,two kinds of Rota-Baxter operators with weighted zero and one for 4-dimensional even and odd twisted Heisenberg Lie superalgebras are computed.