Quantum Group Symmetry and Q-Tensor Algebras
L. C. Biedenharn, M. A. Lohe, "Quantum Group Symmetry and Q-Tensor Algebras"
1995 | pages: 303 | ISBN: 9810223315 | DJVU | 6 mb
1995 | pages: 303 | ISBN: 9810223315 | DJVU | 6 mb
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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