Introduction

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Abstract

This chapter gives a motivation for the use of Hopf algebras and their various generalizations for describing symmetries in diverse situations. This is made possible by their common feature of a closed monoidal structure of the category of modules—lifted from different base categories in each case of the discussed Hopf algebra-like structures. In category theoretical terms, liftings of (closed) monoidal structures to module categories correspond to so-called (Hopf) bimonads. The aim of the book, as summarized in the Introduction, is to give a common interpretation of the apparently different generalizations of Hopf algebra as Hopf monad structures on suitable functors. The covered examples include classical Hopf algebras, Hopf monoids in duoidal (in particular braided monoidal) categories, Hopf algebroids and (in particular) weak Hopf algebras.

Original languageEnglish
Pages (from-to)1-6
Number of pages6
JournalLecture Notes in Mathematics
Volume2226
DOIs
Publication statusPublished - Jan 1 2018

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Hopf Algebra
Weak Hopf Algebra
Closed
Monoidal Category
Monads
Monoids
Functor
Symmetry
Module
Term
Generalization

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Introduction. / Böhm, G.

In: Lecture Notes in Mathematics, Vol. 2226, 01.01.2018, p. 1-6.

Research output: Contribution to journalEditorial

Böhm, G. / Introduction. In: Lecture Notes in Mathematics. 2018 ; Vol. 2226. pp. 1-6.
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