Some Related Studies On N-differential Graded Poisson Algebras

Recently, many interesting generalizations on Poisson algebras have been obtained, such as differential graded Poisson algebra. In this paper, we mainly discuss some related studies on n-differential graded Poisson algebras. The main contents are as follows:In the first part, we describe the purpose of this paper, the main results,prior knowl-edge and so on;In the second part, the notion of n-differential Graded Poisson algebras is given. By studying the tensor product of n-differential Graded Poisson algebras, we prove that the invariance of the tensor extension of n-differential Graded Poisson algebras, moreover, we prove the category of n-differential graded Poisson algebras is a symmetric monoidal category;In the third part, according to the definition of a left differential graded Poisson module, similarly, the notion of a left n-differential graded Poisson module is given. Let A be a n-differential graded Poisson algebra, we can construct a new differential graded algebra B. And we prove that the categories of left n-differential graded Poisson modules over A is isomorphic to the categories of left differential graded modules over B.