الفهرس 
Introduction
CoalgebrasOnly 14 pages are availabe for public view
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Abstract
In this thesis, quantum double structure of extended Heisenberg algebra without qdeformations is presented and quantum double structure of Turaev coalgebra is studied. Also, regular representation of the extended Heisenberg quantum algebra is given. Chapter one contains the basic definitions and structures which are needed through out thesis, such a Hopf algebra structure, its dual structure in a finite dimensional case, and the opposite (coopposite) Hopf algebra structure. Moreover, the Hopf module structure and the regular representation of Hopf algebra is studied. In chapter two, the algebraic structures of both Quantum group and Quantum double are introduced by two approaches. The first approach does not depend on qdeformations [13] in constructing both of them ,while the other one depend on qdeformations [6] . In chapter three, Quantum double of extended Heisenberg algebra without qdeformations is given and its regular representation is deduced. In chapter four, the Quantum Double of Turaev coalgebra structure [23] is studied as a generalization of the quantum double structure.