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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Arithmetik & Algebra Hopf Algebras and Their Generalizations from a Category Theoretical Point of View
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Hopf Algebras and Their Generalizations from a Category Theoretical Point of View
Gabriella Böhm (Taschenbuch, Englisch)
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Beschreibung
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. 48,14 €
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Technische Daten
Erscheinungsdatum
02.11.2018
Sprache
Englisch
EAN
9783319981369
Herausgeber
Springer International Publishing
Serien- oder Bandtitel
Lecture Notes in Mathematics
Sonderedition
Nein
Autor
Gabriella Böhm
Seitenanzahl
165
Auflage
1st edition 2018
Einbandart
Taschenbuch
Schlagwörter
MSC (2010): 16T10, 16T05, 18C15, 18D10, 18D15, bialgebra, Hopf algebra, bialgebroid, Hopf algebroid, weak bialgebra, weak Hopf algebra, bimonad, Hopf monad, monoidal category, duoidal category, Eilenberg-Moore lifting
Thema-Inhalt
PBF - Algebra
Höhe
235 mm
Breite
15.5 cm
Hersteller: Springer, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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