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Hopf Algebras and Their Generalizations from a Category Theoretical Point of View / Gabriella Böhm

By: Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Springer eBook Collection | SpringerLink Bücher | Lecture notes in mathematics ; 2226Publisher: Cham : Springer, [2019]Copyright date: © 2019Edition: Korrigierte PublikationDescription: Online-Ressource (XI, 165 Seiten) : Illustrationen, DiagrammeISBN:
  • 9783319981376
Subject(s): Additional physical formats: 9783319981369 | Erscheint auch als: Hopf algebras and their generalizations from a category theoretical point of view. Druck-Ausgabe Cham, Switzerland : Springer, 2018. xi, 163 SeitenDDC classification:
  • 512.6
MSC: MSC: *16T05 | 18D10 | 16T10 | 18C15 | 18D15RVK: RVK: SI 850LOC classification:
  • QA169
DOI: DOI: 10.1007/978-3-319-98137-6Online resources: Summary: 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-studyPPN: PPN: 1040278787Package identifier: Produktsigel: ZDB-2-LNM | ZDB-2-SEB | ZDB-2-SMA | ZDB-2-SXMS
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