本文關(guān)鍵詞： Hopf π-余代數(shù) Hopf π-余代數(shù)偏作用 偏π-H-余模 偏π-smash積　出處：《曲阜師范大學(xué)》2015年碩士論文　論文類型：學(xué)位論文

【摘要】：Hopfπ-余代數(shù)最初是由Turaev引入的一類代數(shù)結(jié)構(gòu),作為Hopf代數(shù)的一種推廣Hopf π-余代數(shù)引起了廣大數(shù)學(xué)學(xué)者的研究興趣并被深入研究,經(jīng)過研究,Hopf代數(shù)上的許多重要結(jié)論在Hopfπ-余代數(shù)上同樣是成立的.群的偏作用是由R.Exel所定義的一類特殊的群作用,并且很快就成為了研究希爾伯特空間上部分等距生成的C*-代數(shù)的有效工具,并且隨著研究的深入,偏群作用已成為環(huán)論中的一個(gè)獨(dú)立且相當(dāng)重要的分支.本文基于以上背景,做了以下幾個(gè)方面的工作.首先我們給出了Hopfπ-余代數(shù)的扁作用的定義,除此之外,我們還給出了偏Hopfπ-余模等一系列的概念.在此之后,我們給出了偏π-H-余模張量積的概念,并證明兩個(gè)偏π-H-余模的張量積還是偏π-H-余模.最后,我們給出了偏π-smash積的定義,并嘗試構(gòu)造了一類Morita關(guān)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.
【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】：2015
【分類號(hào)】：O153.3

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相關(guān)期刊論文 前1條

1 ;L-R smash products for bimodule algebras[J];Progress in Natural Science;2006年06期

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本文編號(hào)：1476553