Hopf algebras and their generalizations from a category theoretical point of view

Bibliographic Information

Hopf algebras and their generalizations from a category theoretical point of view

Gabriella Böhm

(Lecture notes in mathematics, 2226)

Springer, c2018

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Note

Includes bibliographical references (p. 155-159) and index

Description and Table of Contents

Description

These lecture notes provide a self-contained introduction to a wide range of generalizations of Hopf algebras. Multiplication of their modules is described by replacing the category of vector spaces with more general monoidal categories, thereby extending the range of applications. Since Sweedler's work in the 1960s, Hopf algebras have earned a noble place in the garden of mathematical structures. Their use is well accepted in fundamental areas such as algebraic geometry, representation theory, algebraic topology, and combinatorics. Now, similar to having moved from groups to groupoids, it is becoming clear that generalizations of Hopf algebras must also be considered. This book offers a unified description of Hopf algebras and their generalizations from a category theoretical point of view. The author applies the theory of liftings to Eilenberg-Moore categories to translate the axioms of each considered variant of a bialgebra (or Hopf algebra) to a bimonad (or Hopf monad) structure on a suitable functor. Covered structures include bialgebroids over arbitrary algebras, in particular weak bialgebras, and bimonoids in duoidal categories, such as bialgebras over commutative rings, semi-Hopf group algebras, small categories, and categories enriched in coalgebras. Graduate students and researchers in algebra and category theory will find this book particularly useful. Including a wide range of illustrative examples, numerous exercises, and completely worked solutions, it is suitable for self-study.

Table of Contents

- Introduction. - Lifting to Eilenberg-Moore Categories. - (Hopf) Bimonads. - (Hopf) Bialgebras. - (Hopf) Bialgebroids. - Weak (Hopf) Bialgebras. - (Hopf) Bimonoids in Duoidal Categories. - Solutions to the Exercises.

by "Nielsen BookData"

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Details

  • NCID
    BB27150592
  • ISBN
    • 9783319981369
  • LCCN
    9783319981
    2018951456
  • Country Code
    sz
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    [Cham]
  • Pages/Volumes
    xi, 163 p.
  • Size
    24 cm
  • Parent Bibliography ID
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