Hopf Algebras and Their Generalizations from a Category Theoretical Point of View / Lecture Notes in Mathematics Bd.2226 (PDF)

Name: Hopf Algebras and Their Generalizations from a Category Theoretical Point of View / Lecture Notes in Mathematics Bd.2226
Brand: Springer-Verlag GmbH
SKU: 108076073
Price: 16.49 EUR
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(Sprache: Englisch)

Autor: Gabriella Böhm

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Hopf Algebras and Their Generalizations from a Category Theoretical Point of View / Lecture Notes in Mathematics Bd.2226, Gabriella Böhm

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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...

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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.

Autoren-Porträt von Gabriella Böhm

Gabriella Böhm received her master's degree in 1993, and a PhD in 1999 from the Eötvös University in Budapest. She has a broad expertise in generalizations of Hopf algebra, and has made significant contributions to the theory of Hopf algebroids as one of the inventors of weak Hopf algebra. The key feature of her work is the use of category theoretical methods in treating algebraic questions.

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Autor: Gabriella Böhm
2018, 1st ed. 2018, 165 Seiten, Englisch
Verlag: Springer-Verlag GmbH
ISBN-10: 3319981374
ISBN-13: 9783319981376
Erscheinungsdatum: 01.11.2018

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