Examples of tensor categories
type: Item
instance of: scholarly article
title: Examples of tensor categories
zbMATH Open document ID: 0784.18003
DOI: 10.1007/BF01232042
author: Sergei Gelfand
author: David Kazhdan
published in: Inventiones Mathematicae
publication date: 1993-06-29T00:00:00Z
full work available at URL: https://eudml.org/doc/144036
review text: \textit{P. Deligne} [Grothendieck Festschrift, Vol. II, Prog. Math. 87, 111- 195 (1990; Zbl 0727.14010)] characterized those \(k\)-linear tensor categories of the form \(\text{Rep}(G)\) for some proalgebraic group scheme \(G\) over a field \(k\) of characteristic zero. Using quotients (by ideals) of subcategories of categories of representations of algebraic Chevalley groups, the authors show that this characterization does not work for \(k\) of positive characteristic. They describe how to correct Deligne's result in this case. They also construct interesting examples of semisimple braided tensor categories as quotients of categories of representations of Hopf algebras (quantum groups) over the ring of integers in a cyclotomic field.
Mathematics Subject Classification ID: 18D10
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 20G05
zbMATH DE Number: 220752
zbMATH Keywords: Tannaka duality
zbMATH Keywords: braiding
zbMATH Keywords: quantum groups
zbMATH Keywords: categories of representations of algebraic Chevalley groups
zbMATH Keywords: semisimple braided tensor categories
zbMATH Keywords: categories of representations of Hopf algebras
reviewed by: Ross H. Street
MaRDI profile type: Publication
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OpenAlex ID: W1978041710
description: scientific article; zbMATH DE number 220752