الفهرس 
Introduction
Quasitriangular Hopf algebrasOnly 14 pages are availabe for public view
 |  | from | 176 |  |  |
| | | from | 176 | | |
Abstract
The aim of this thesis is to study the structure of the graded Hopf algebras . Also , we have studied a new structure which is called’ graded QuasiHopf algebras’. Finally we have studied the concept of quantum group in the graded version from both the quantum double point of view and the deformation theory point of view . The substance of the thesis is divided into five chapters : Chapter I : We will give some basic facts about the Lie algebras , Hopf algebras and quasiHopf algebras . Also , we introduce some basic concepts about Hopf groupcoalgebra theory . Chapter II : contains some facts about the quantum group theory from both quantum double and deformation theory points of views . Chapter III : This Chapter consists of three sections . The main goal of this chapter is to study some new facts about the structure of the graded Hopf algebras .Moreover , we will give the new concept of the graded QuasiHopf algebras which is a generlization to the concept of QuasiHopf algebras . On the other hand , we can consider the graded QuasiHopf algebras are a generlization to the graded Hopf algebras . Chapter IV : we will establish the structure of the graded quantum group as quantum double for a groupgraded Hopf algebra . The main purpose of section(4.1) is studying some details about the duality of Groupgraded Hopf algebras . In section (4.2) we bring the results of the quasitriangular Hopf algebras to the more general framework of groupgraded Hopf algebras . Finally , in section (4.3) , we will establish the structure of the quantum double for a groupgraded Hopf algebra . Chapter V In this chapter we concentrate on studying the graded version of the quantum groups from deformation point of view . In section (5.1) we studied the concept of the Hopf pairing in both usual and graded cases. In section (5.2) we give a method of defining a quasitriangular Hopf coalgebra from a Hopf algebra endowed with an action of a group by Hopf automorphisms . Finally , in section (5.3) , the graded quantum groups have considered in our studies .