Description

Book Synopsis
Provides an introduction to Hopf algebras in braided monoidal categories with applications to Hopf algebras in the usual sense. The main goal is to present from scratch and with complete proofs the theory of Nichols algebras (or quantum symmetric algebras) and the surprising relationship between Nichols algebras and generalized root systems.

Table of Contents
  • Hopf algebras, Nichols algebras, braided monoidal categories, and quantized enveloping algebras: A quick introduction to Nichols algebras
  • Basic Hopf algebra theory
  • Braided monoidal categories
  • Yetter-Drinfeld modules over Hopf algebras
  • Gradings and filtrations
  • Braided structures
  • Nichols algebras
  • Quantized enveloping algebras and generalizations
  • Cartan graphs, Weyl groupoids, and root systems: Cartan graphs and Weyl groupoids
  • The structure of Cartan graphs and root systems
  • Cartan graphs of Lie superalgebras
  • Weyl groupoids and root systems of Nichols algebras: A braided monoidal isomorphism of Yetter-Drinfeld modules
  • Nichols systems, and semi-Cartan graph of Nichols algebras
  • Right coideal subalgebras of Nichols systems, and Cartan graph of Nichols algebras
  • Applications: Nichols algebras of diagonal type
  • Nichols algebras of Cartan type
  • Nichols algebras over non-abelian groups
  • Bibliography
  • Index of symbols
  • Subject index.

    Hopf Algebras and Root Systems

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      £109.80

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      RRP £122.00 – you save £12.20 (10%)

      Order before 4pm tomorrow for delivery by Sat 8 Aug 2026.

      A Hardback by Istvan Heckenberger, Hans-Jurgen Schneider

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        Publisher: MP-AMM American Mathematical
        Publication Date: Publication Date: 8/30/2020 12:00:00 AM
        ISBN13: 9781470452322, 978-1470452322
        ISBN10: 1470452324

        Description

        Book Synopsis
        Provides an introduction to Hopf algebras in braided monoidal categories with applications to Hopf algebras in the usual sense. The main goal is to present from scratch and with complete proofs the theory of Nichols algebras (or quantum symmetric algebras) and the surprising relationship between Nichols algebras and generalized root systems.

        Table of Contents
        • Hopf algebras, Nichols algebras, braided monoidal categories, and quantized enveloping algebras: A quick introduction to Nichols algebras
        • Basic Hopf algebra theory
        • Braided monoidal categories
        • Yetter-Drinfeld modules over Hopf algebras
        • Gradings and filtrations
        • Braided structures
        • Nichols algebras
        • Quantized enveloping algebras and generalizations
        • Cartan graphs, Weyl groupoids, and root systems: Cartan graphs and Weyl groupoids
        • The structure of Cartan graphs and root systems
        • Cartan graphs of Lie superalgebras
        • Weyl groupoids and root systems of Nichols algebras: A braided monoidal isomorphism of Yetter-Drinfeld modules
        • Nichols systems, and semi-Cartan graph of Nichols algebras
        • Right coideal subalgebras of Nichols systems, and Cartan graph of Nichols algebras
        • Applications: Nichols algebras of diagonal type
        • Nichols algebras of Cartan type
        • Nichols algebras over non-abelian groups
        • Bibliography
        • Index of symbols
        • Subject index.

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