微分分次泊松余代数和余模
发布时间：2018-10-21 07:49
【摘要】：本文引入了微分分次泊松余代数的概念,即将微分分次余代数与分次泊松余代数结合起来.首先我们回顾分次余代数和分次李余代数的一些基本定义,在此基础上延伸出微分分次余代数和分次泊松余代数的概念,然后我们将两者结合给出微分分次泊松余代数的定义.在给出定义之后,我们具体讨论了微分分次泊松余代数的一些基本性质.如一个微分分次泊松余代数的反余代数也是微分分次泊松余代数,两个微分分次泊松余代数的张量积也是微分分次泊松余代数,微分分次泊松余代数范畴是一个带有对称单位对象的独异范畴.讨论完余代数的性质,在此基础上,自然地考虑到余代数的余模结构,我们首先根据余代数结构给出微分分次泊松余模的定义,其余模结构与微分分次泊松代数的模结构是对偶的,然后讨论微分分次泊松余模的性质.如两个微分分次泊松余代数的右余模的张量积是两个余代数的张量积的右余模.在本文的最后,我们给出了微分分次泊松余代数的泛包络余代数的定义,并给出一些泛包络余代数的一般性质.
[Abstract]:In this paper, the concept of differential graded Poisson coalgebra is introduced, which combines differential graded coalgebra with graded Poisson coalgebra. First, we review some basic definitions of graded coalgebras and graded lie coalgebras, and then extend the concepts of differential graded coalgebras and graded Poisson coalgebras. Then we combine them to give the definitions of differential graded Poisson coalgebras. After giving the definition, we discuss some basic properties of differential graded Poisson coalgebra. For example, the inverse coalgebra of a differential graded Poisson coalgebra is also a differential graded Poisson coalgebra, and the tensor product of two differential graded Poisson coalgebras is also a differential graded Poisson coalgebra. The category of differential graded Poisson coalgebra is an unique category with symmetric unit object. In this paper, we discuss the properties of coalgebras. On this basis, we naturally consider the structure of comodules of coalgebras. We first give the definition of differential graded Poisson comodules according to the structure of coalgebras. The other module structures and the module structures of differential graded Poisson algebras are dual. Then the properties of differential graded Poisson comodules are discussed. For example, the tensor product of the right comodules of two differential graded Poisson coalgebras is the right comodule of the tensor product of two coalgebras. At the end of this paper, we give the definition of universal envelope coalgebra of differential graded Poisson coalgebra, and give some general properties of universal envelope coalgebra.
【学位授予单位】：曲阜师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O153.3
本文编号：2284434
[Abstract]:In this paper, the concept of differential graded Poisson coalgebra is introduced, which combines differential graded coalgebra with graded Poisson coalgebra. First, we review some basic definitions of graded coalgebras and graded lie coalgebras, and then extend the concepts of differential graded coalgebras and graded Poisson coalgebras. Then we combine them to give the definitions of differential graded Poisson coalgebras. After giving the definition, we discuss some basic properties of differential graded Poisson coalgebra. For example, the inverse coalgebra of a differential graded Poisson coalgebra is also a differential graded Poisson coalgebra, and the tensor product of two differential graded Poisson coalgebras is also a differential graded Poisson coalgebra. The category of differential graded Poisson coalgebra is an unique category with symmetric unit object. In this paper, we discuss the properties of coalgebras. On this basis, we naturally consider the structure of comodules of coalgebras. We first give the definition of differential graded Poisson comodules according to the structure of coalgebras. The other module structures and the module structures of differential graded Poisson algebras are dual. Then the properties of differential graded Poisson comodules are discussed. For example, the tensor product of the right comodules of two differential graded Poisson coalgebras is the right comodule of the tensor product of two coalgebras. At the end of this paper, we give the definition of universal envelope coalgebra of differential graded Poisson coalgebra, and give some general properties of universal envelope coalgebra.
【学位授予单位】：曲阜师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O153.3
【参考文献】
相关期刊论文 前1条
1 L JiaFeng;WANG XingTing;ZHUANG GuangBin;;DG Poisson algebra and its universal enveloping algebra[J];Science China(Mathematics);2016年05期
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