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Quantum Groups

Quantum Groups
A Path to Current Algebra

$74.00

Part of Australian Mathematical Society Lecture Series

  • Date Published: January 2007
  • availability: Available
  • format: Paperback
  • isbn: 9780521695244

$74.00
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About the Authors
  • Algebra has moved well beyond the topics discussed in standard undergraduate texts on 'modern algebra'. Those books typically dealt with algebraic structures such as groups, rings and fields: still very important concepts! However Quantum Groups: A Path to Current Algebra is written for the reader at ease with at least one such structure and keen to learn algebraic concepts and techniques. A key to understanding these new developments is categorical duality. A quantum group is a vector space with structure. Part of the structure is standard: a multiplication making it an 'algebra'. Another part is not in those standard books at all: a comultiplication, which is dual to multiplication in the precise sense of category theory, making it a 'coalgebra'. While coalgebras, bialgebras and Hopf algebras have been around for half a century, the term 'quantum group', along with revolutionary new examples, was launched by Drinfel'd in 1986.

    • Essential for any graduate student or researcher whose research involves quantum groups
    • Containing the latest algebraic concepts and techniques, this book updates the meaning of 'modern algebra'
    • Includes over 60 worked examples and exercises
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    Reviews & endorsements

    "The book is very well written [and] it is quite concise."
    E.J. Taft, Mathematical Reviews

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    Product details

    • Date Published: January 2007
    • format: Paperback
    • isbn: 9780521695244
    • length: 160 pages
    • dimensions: 229 x 152 x 9 mm
    • weight: 0.24kg
    • contains: 26 b/w illus. 25 exercises
    • availability: Available
  • Table of Contents

    Introduction
    1. Revision of basic structures
    2. Duality between geometry and algebra
    3. The quantum general linear group
    4. Modules and tensor products
    5. Cauchy modules
    6. Algebras
    7. Coalgebras and bialgebras
    8. Dual coalgebras of algebras
    9. Hopf algebras
    10. Representations of quantum groups
    11. Tensor categories
    12. Internal homs and duals
    13. Tensor functors and Yang-Baxter operators
    14. A tortile Yang-Baxter operator for each finite-dimensional vector space
    15. Monoids in tensor categories
    16. Tannaka duality
    17. Adjoining an antipode to a bialgebra
    18. The quantum general linear group again
    19. Solutions to exercises
    References
    Index.

  • Author

    Ross Street, Macquarie University, Sydney
    Ross Street is a Professor of Mathematics and Director of the Centre of Australian Category Theory at Macquarie University. He is also a Fellow of the Australian Academy of Science.

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