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  3. Quantum Groups
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    • Publisher:
      Cambridge University Press
      Publication date:
      December 2009
      January 2007
      ISBN:
      9780511618505
      9780521695244
      DOI:
      https://doi.org/10.1017/CBO9780511618505
      Dimensions:
      Weight & Pages:
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.24kg, 160 Pages
      • Subjects:
      Mathematics (general), Mathematics, Physics and Astronomy, Logic, Categories and Sets, Theoretical Physics and Mathematical Physics
      Series:
      Australian Mathematical Society Lecture Series (19)
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    • Selected: Digital
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    Subjects:
    Mathematics (general), Mathematics, Physics and Astronomy, Logic, Categories and Sets, Theoretical Physics and Mathematical Physics
    Series:
    Australian Mathematical Society Lecture Series (19)
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    Book description

    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.

    Reviews

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

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