發(fā)布時(shí)間：2018-10-21 07:49

【摘要】：本文引入了微分分次泊松余代數(shù)的概念,即將微分分次余代數(shù)與分次泊松余代數(shù)結(jié)合起來(lái).首先我們回顧分次余代數(shù)和分次李余代數(shù)的一些基本定義,在此基礎(chǔ)上延伸出微分分次余代數(shù)和分次泊松余代數(shù)的概念,然后我們將兩者結(jié)合給出微分分次泊松余代數(shù)的定義.在給出定義之后,我們具體討論了微分分次泊松余代數(shù)的一些基本性質(zhì).如一個(gè)微分分次泊松余代數(shù)的反余代數(shù)也是微分分次泊松余代數(shù),兩個(gè)微分分次泊松余代數(shù)的張量積也是微分分次泊松余代數(shù),微分分次泊松余代數(shù)范疇是一個(gè)帶有對(duì)稱單位對(duì)象的獨(dú)異范疇.討論完余代數(shù)的性質(zhì),在此基礎(chǔ)上,自然地考慮到余代數(shù)的余模結(jié)構(gòu),我們首先根據(jù)余代數(shù)結(jié)構(gòu)給出微分分次泊松余模的定義,其余模結(jié)構(gòu)與微分分次泊松代數(shù)的模結(jié)構(gòu)是對(duì)偶的,然后討論微分分次泊松余模的性質(zhì).如兩個(gè)微分分次泊松余代數(shù)的右余模的張量積是兩個(gè)余代數(shù)的張量積的右余模.在本文的最后,我們給出了微分分次泊松余代數(shù)的泛包絡(luò)余代數(shù)的定義,并給出一些泛包絡(luò)余代數(shù)的一般性質(zhì).
[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.
【學(xué)位授予單位】：曲阜師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O153.3

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

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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本文編號(hào)：2284434