Biedenharn L.C., Lohe M.A. Quantum Group Symmetry and Q-Tensor Algebras

World Scientific, 1995. — 303 p. — ISBN: 9810223315.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.Origins of Quantum Groups
Representations of Unitary Quantum Groups
Tensor Operators in Quantum Groups
The Dual Algebra and the Factor Group
Quantum Rotation Matrices
Quantum Groups at Roots of Unity
Algebraic Induction of Quantum Group Representations
Special Topics