Formal Hopf algebra theory. I: Hopf modules for pseudomonoids
type: Item
instance of: scholarly article
title: Formal Hopf algebra theory. I: Hopf modules for pseudomonoids
zbMATH Open document ID: 1165.18006
author: Ignacio López Franco
published in: Journal of Pure and Applied Algebra
publication date: 2009-03-30T00:00:00Z
review text: Formal similarities between an antipode for a bialgebra and a dualization functor for a monoidal category were clarified in the article of \textit{B. Day, P. McCrudden} and \textit{R. Street} [``Dualizations and antipodes'', Appl. Categ. Struct. 11, No.~3, 229--260 (2003; Zbl 1137.18302)] via the notion of autonomous pseudomonoid in a monoidal bicategory. The author's goal in this and subsequent papers is to generalize various theorems on Hopf algebras to autonomous pseudomonoids and so to obtain other applications. This paper concentrates on the structure theorem for Hopf modules proved in \textit{R. G. Larson} and \textit{M. E. Sweedler} [``An associative orthogonal bilinear form for Hopf algebras'', Am. J. Math. 91, 75--94 (1969; Zbl 0179.05803)] and the quasi-Hopf algebra version in \textit{P. Schauenburg} [``Two characterizations of finite quasi-Hopf algebras'', J. Algebra 273, No.~2, 538--550 (2004; Zbl 1041.16032)]. More precisely, the author shows that a map pseudomonoid has a left dualization if and only if it satisfies an appropriate version of the fundamental theorem of Hopf modules. He also shows great skill at working in a monoidal bicategory.
reviewed by: Ross H. Street
Mathematics Subject Classification ID: 18D05
Mathematics Subject Classification ID: 16W30
zbMATH DE Number: 5534974
zbMATH Keywords: pseudomonoid
zbMATH Keywords: monoidal bicategory
zbMATH Keywords: Hopf algebra
zbMATH Keywords: rigid monoidal category
zbMATH Keywords: autonomous monoidal category
MaRDI profile type: Publication
full work available at URL: j.jpaa.2008.11.005
OpenAlex ID: W2091055854
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DOI: 10.1016/J.JPAA.2008.11.005
description: scientific article; zbMATH DE number 5534974