Hopf群余代数的偏（余）作用

发布时间：2018-01-30 15:22

本文关键词： Hopf π-余代数 Hopf π-余代数偏作用偏π-H-余模偏π-smash积　出处：《曲阜师范大学》2015年硕士论文　论文类型：学位论文

【摘要】：Hopfπ-余代数最初是由Turaev引入的一类代数结构,作为Hopf代数的一种推广Hopf π-余代数引起了广大数学学者的研究兴趣并被深入研究,经过研究,Hopf代数上的许多重要结论在Hopfπ-余代数上同样是成立的.群的偏作用是由R.Exel所定义的一类特殊的群作用,并且很快就成为了研究希尔伯特空间上部分等距生成的C*-代数的有效工具,并且随着研究的深入,偏群作用已成为环论中的一个独立且相当重要的分支.本文基于以上背景,做了以下几个方面的工作.首先我们给出了Hopfπ-余代数的扁作用的定义,除此之外,我们还给出了偏Hopfπ-余模等一系列的概念.在此之后,我们给出了偏π-H-余模张量积的概念,并证明两个偏π-H-余模的张量积还是偏π-H-余模.最后,我们给出了偏π-smash积的定义,并尝试构造了一类Morita关系.
[Abstract]:Hopf 蟺 -coalgebras were initially introduced by Turaev as a class of algebraic structures. As a generalization of Hopf algebra, Hopf 蟺 -coalgebra has attracted the interest of many mathematics scholars and has been deeply studied. Many important conclusions on Hopf algebras are also true on Hopf 蟺 -coalgebras. The partial action of groups is a kind of special group action defined by R. Exel. And soon became the research Hilbert space partial isometric generation of Ca-algebra effective tool, and with the depth of the study. Partial group action has become an independent and important branch of ring theory. Based on the above background, we do the following work. Firstly, we give the definition of the flat action of Hopf 蟺 -coalgebra. In addition, we also give a series of concepts such as partial Hopf 蟺 -comodules. After that, we give the concept of partial 蟺 -H-comodule tensor product. It is proved that the tensor product of two partial 蟺 -H-comodules is a partial 蟺 -H-comodule. Finally, we give the definition of partial 蟺 -smash product and try to construct a kind of Morita relation.
【学位授予单位】：曲阜师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O153.3

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