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Quantum Groups
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Details

  • 26 b/w illus. 25 exercises
  • Page extent: 160 pages
  • Size: 228 x 152 mm
  • Weight: 0.24 kg

Library of Congress

  • Dewey number: 512/.55
  • Dewey version: 22
  • LC Classification: QC20.7.G76 S87 2007
  • LC Subject headings:
    • Quantum groups
    • Algebra

Library of Congress Record

Paperback

 (ISBN-13: 9780521695244)

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

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.

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