(Hopf) bialgebras

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

Interpreting Hopf algebras and their various generalizations as Hopf monads begins in this chapter with classical Hopf algebras over fields. Endofunctors on the category of vector spaces are considered, which are induced by taking the tensor product with a fixed vector space. The algebra structures on this vector space are related to the monad structures on the induced functor; and the coalgebra structures are related to the opmonoidal structures. This results in a bijection between the bialgebras; and the induced bimonads on the category of vector spaces. The bijection is shown to restrict to Hopf algebras on one hand; and Hopf monads on the other hand.

Original languageEnglish
Title of host publicationLecture Notes in Mathematics
PublisherSpringer Verlag
Pages47-58
Number of pages12
DOIs
Publication statusPublished - Jan 1 2018

Publication series

NameLecture Notes in Mathematics
Volume2226
ISSN (Print)0075-8434

ASJC Scopus subject areas

  • Algebra and Number Theory

Fingerprint Dive into the research topics of '(Hopf) bialgebras'. Together they form a unique fingerprint.

  • Cite this

    Böhm, G. (2018). (Hopf) bialgebras. In Lecture Notes in Mathematics (pp. 47-58). (Lecture Notes in Mathematics; Vol. 2226). Springer Verlag. https://doi.org/10.1007/978-3-319-98137-6_4