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  3. New Directions in Hopf Algebras
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  • Publisher:
    Cambridge University Press
    Publication date:
    25 June 2025
    06 May 2002
    ISBN:
    9781009701396
    9780521815123
    9780521124317
    DOI:
    https://doi.org/10.1017/9781009701396
    Dimensions:
    (234 x 156 mm)
    Weight & Pages:
    0.823kg, 496 Pages
    Dimensions:
    (234 x 156 mm)
    Weight & Pages:
    0.69kg, 496 Pages
    • Subjects:
    Mathematics, Real and Complex Analysis, Algebra
    Series:
    Mathematical Sciences Research Institute Publications
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    • Selected: Digital
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    Subjects:
    Mathematics, Real and Complex Analysis, Algebra
    Series:
    Mathematical Sciences Research Institute Publications
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    Book description

    Hopf algebras have important connections to quantum theory, Lie algebras, knot and braid theory, operator algebras and other areas of physics and mathematics. They have been intensely studied in the past; in particular, the solution of a number of conjectures of Kaplansky from the 1970s has led to progress on the classification of semisimple Hopf algebras and on the structure of pointed Hopf algebras. Among the topics covered are results toward the classification of finite-dimensional Hopf algebras (semisimple and non-semisimple), as well as what is known about the extension theory of Hopf algebras. Some papers consider Hopf versions of classical topics, such as the Brauer group, while others are closer to work in quantum groups. The book also explores the connections and applications of Hopf algebras to other fields.

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