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Quantum Group Symmetry And Q-tensor Algebras, PDF eBook

Quantum Group Symmetry And Q-tensor Algebras PDF

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Quantum groups are a generalization of the classical Lie groups and Lie algebras and provide a natural extension of the concept of symmetry fundamental to physics.

This monograph is a survey of the major developments in quantum groups, using an original approach based on the fundamental concept of a tensor operator.

Using this concept, properties of both the algebra and co-algebra are developed from a single uniform point of view, which is especially helpful for understanding the noncommuting co-ordinates of the quantum plane, which we interpret as elementary tensor operators.

Representations of the q-deformed angular momentum group are discussed, including the case where q is a root of unity, and general results are obtained for all unitary quantum groups using the method of algebraic induction.

Tensor operators are defined and discussed with examples, and a systematic treatment of the important (3j) series of operators is developed in detail.

This book is a good reference for graduate students in physics and mathematics.

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