自主和带状独异Hom-Hopf代数

发布时间：2018-04-06 22:24

本文选题：自主独异Hom-Hopf代数　切入点：带状独异Hom-Hopf代数　出处：《曲阜师范大学》2017年硕士论文

【摘要】：本文中我们研究了有限维独异Hom-Hopf代数上的自主结构,并且定义了(余)自主独异Hom-Hopf代数,然后给出了在有双射对极的有限维拟三角独异Hom-Hopf代数(H,α,R)上定义带状结构的一个充分必要条件.全文共分五节:第一、二节为本文的引言与预备知识.第三节先给出了自主独异Hom-Hopf代数(H,α)的定义,然后研究了其上的表示范畴Rep(H),证明了:(H,α)是一个自主独异Hom-Hopf代数当且仅当Rep(H)是一个自主范畴.第四节是第三节的对偶,给出了余自主独异Hom-Hopf代数的定义并证明了:(H,α)是一个余自主独异Hom-Hopf代数当且仅当Corep(H)是一个自主范畴.第五节给出了在有双射对极的有限维拟三角独异Hom-Hopf代数(H,α,R)上定义带状结构的一个充分必要条件.
[Abstract]:In this paper, we study the autonomous structures on finite-dimensional unique Hom-Hopf algebras, and define (cooperative-independent Hom-Hopf algebras).Then a sufficient and necessary condition for the definition of banded structures on a finite-dimensional quasi trigonometric solitary Hom-Hopf algebra with a bijective pair is given.The full text is divided into five sections: the first and second are the introduction and preparatory knowledge of this paper.In the third section, we first give the definition of the autonomous unique Hom-Hopf algebra H, 伪), then we study the representation category Repan H on it, and prove that the representation category Repan H, 伪) is an autonomous unique Hom-Hopf algebra if and only if it is an autonomous category.The fourth section is the duality of the third section. The definition of the coautonomous unique Hom-Hopf algebra is given and it is proved that the Hom-Hopf algebra is a coautonomous unique Hom-Hopf algebra if and only if it is an autonomous category.In section 5, we give a necessary and sufficient condition for the definition of banded structures on finite dimensional quasi trigonometric solitary Hom-Hopf algebras with bijective dipoles.
【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

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