Quantum groups: a path to current algebra

    Research output: Book/ReportBookpeer-review

    Abstract

    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 the latest 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.
    Original languageEnglish
    Place of PublicationCambridge
    PublisherCambridge University Press
    ISBN (Print)9780521695244
    Publication statusPublished - 2007

    Publication series

    NameAustralian Mathematical Society lecture series
    PublisherCambridge University Press
    Volume19

    Keywords

    • Quantum groups
    • Algebra

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