Quantum group symmetry and q-tensor algebras

Bibliographic Information

Quantum group symmetry and q-tensor algebras

L.C. Biedenharn, M.A. Lohe

World Scientific, c1995

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Note

Includes bibliographical references (p. 275-289) and index

Description and Table of Contents

Description

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.

Table of Contents

  • 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.

by "Nielsen BookData"

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