Titlebook: Quantum Groups and Their Representations; Anatoli Klimyk,Konrad Schmüdgen Book 1997 Springer-Verlag Berlin Heidelberg 1997 Vector space.al

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Theoretical and Mathematical Physicshttp://image.papertrans.cn/q/image/781224.jpg

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978-3-642-64601-0Springer-Verlag Berlin Heidelberg 1997

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Hopf Algebrasultiplication, a counit and an antipode. In some appropriate sense, these structures and their axioms reflect the multiplication, the unit element and the inverse elements of a group and their corresponding properties.

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-Calculustric functions, and .-orthogonal polynomials). This chapter gives a brief introduction to these topics. The notions and facts developed below will be needed at various places in the book, but they are also of interest in themselves.

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Drinfeld-Jimbo Algebrastures and results on these algebras such as the Poincaré-Birkhoff-Witt theorem, braid group actions, Verma modules, quantum Killing forms, quantum Casimir elements, centers and Harish-Chandra homomorphisms.

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The Quantum Group ,(2) and Its RepresentationsIn this chapter we investigate the coordinate Hopf algebra of the quantum group .(2) and develop its corepresentation theory. It is the simplest example from the series of quantum groups associated with simple complex Lie groups which will be studied extensively in the second part of the book.

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