Quantum group symmetry and q-tensor algebras
著者
書誌事項
Quantum group symmetry and q-tensor algebras
World Scientific, c1995
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注記
Includes bibliographical references (p. 275-289) and index
内容説明・目次
内容説明
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.
目次
- Origins of quantum groups
- representations of unitary quantum groups
- tensor operators in quantum groups
- the dual algebra and the factor group
- rotation functions for SUq(2)
- quantum groups at roots of unity
- algebraic induction of quantum group representations
- special topics.
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