Rota-Baxter Operators On Hamiltonian Algebras And Heisenberg Superalgebras

Rota-Baxter operators theory is the active area of research in mathematics and physics. Let F be an algebraic closed field of characteristic0. In this paper, we char-acterize the Rota-Baxter operators on two classifications of algebras, which type of algebra is Hamiltonian algebras, they are associative algebras; Another type of algebra is Heisenberg superalgebras, they are (non-associative) Lie superalgebras. First of all, we employ the classification theorem of Hamiltonian algebras, character-izing all the Rota-Baxter operators of any weight on finite dimensional Hamiltonian algebras by means of computation. Then, we employ the classification method of the central element of Heisenberg superalgebras, characterizing all the Rota-Baxter operators of any weight on three-dimensional and four-dimensional Heisenberg su-peralgebras by means of computation.