Tannaka-Krein duality for Hopf algebroids
type: Item
instance of: scholarly article
title: Tannaka-Krein duality for Hopf algebroids
zbMATH Open document ID: 1169.18003
published in: Israel Journal of Mathematics
publication date: 2009-02-17T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0206113
review text: For a ring \(R\), this paper uses the notion of \(R\)-coalgebroid defined by \textit{M. Takeuchi} [``\(\sqrt{\text{Morita}}\) theory: Formal ring laws and monoidal equivalences of categories of bimodules'', J. Math. Soc. Japan 39, 301--336 (1987; Zbl 0619.16032)] which have a counit and comultiplication on an underlying double \(R\)-bimodule. An \(R\)-bialgebroid is then a monoid in the monoidal category of \(R\)-coalgebroids; it is a Hopf algebroid when its category of finitely generated projective comodules is autonomous (rigid, compact). The paper develops Tannaka-Krein duality for Hopf algebroids and strong monoidal functors into the category of dual \(R\)-bimodules.
reviewed by: Ross H. Street
Mathematics Subject Classification ID: 18D10
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 17B37
zbMATH DE Number: 5508707
zbMATH Keywords: double bimodule
zbMATH Keywords: fibre functor
zbMATH Keywords: coalgebroid
zbMATH Keywords: Hopf algebroid
zbMATH Keywords: Tannaka duality
author: Phùng Hô Hai
MaRDI profile type: Publication
OpenAlex ID: W2110728416
arXiv ID: math/0206113
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DOI: 10.1007/S11856-008-1047-5
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description: scientific article