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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.
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.
First book to provide a unified category theoretical description of apparently different generalizations of Hopf algebras (including Hopf algebroids, weak Hopf algebras, and Hopf bimonoids in duoidal categories)
Includes fully worked solutions to the exercises
Enjoys a rigorous Bourbaki-style presentation, supplemented with various examples
| Erscheinungsjahr: | 2018 |
|---|---|
| Fachbereich: | Arithmetik & Algebra |
| Genre: | Mathematik, Medizin, Naturwissenschaften, Technik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Inhalt: |
xi
165 S. 239 s/w Illustr. 165 p. 239 illus. |
| ISBN-13: | 9783319981369 |
| ISBN-10: | 3319981366 |
| Sprache: | Englisch |
| Herstellernummer: | 978-3-319-98136-9 |
| Einband: | Kartoniert / Broschiert |
| Autor: | Böhm, Gabriella |
| Auflage: | 1st edition 2018 |
| Hersteller: | Springer International Publishing |
| Verantwortliche Person für die EU: | Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com |
| Maße: | 235 x 155 x 11 mm |
| Von/Mit: | Gabriella Böhm |
| Erscheinungsdatum: | 02.11.2018 |
| Gewicht: | 0,283 kg |
First book to provide a unified category theoretical description of apparently different generalizations of Hopf algebras (including Hopf algebroids, weak Hopf algebras, and Hopf bimonoids in duoidal categories)
Includes fully worked solutions to the exercises
Enjoys a rigorous Bourbaki-style presentation, supplemented with various examples
| Erscheinungsjahr: | 2018 |
|---|---|
| Fachbereich: | Arithmetik & Algebra |
| Genre: | Mathematik, Medizin, Naturwissenschaften, Technik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Inhalt: |
xi
165 S. 239 s/w Illustr. 165 p. 239 illus. |
| ISBN-13: | 9783319981369 |
| ISBN-10: | 3319981366 |
| Sprache: | Englisch |
| Herstellernummer: | 978-3-319-98136-9 |
| Einband: | Kartoniert / Broschiert |
| Autor: | Böhm, Gabriella |
| Auflage: | 1st edition 2018 |
| Hersteller: | Springer International Publishing |
| Verantwortliche Person für die EU: | Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com |
| Maße: | 235 x 155 x 11 mm |
| Von/Mit: | Gabriella Böhm |
| Erscheinungsdatum: | 02.11.2018 |
| Gewicht: | 0,283 kg |
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