Generic modules over the quantum group \(U_t(sl(2))\) at \(t\) a root of unit
type: Item
instance of: scholarly article
title: Generic modules over the quantum group \(U_t(sl(2))\) at \(t\) a root of unit
zbMATH Open document ID: 0813.17008
DOI: 10.1007/BF02567601
author: Jie Xiao
published in: Manuscripta Mathematica
publication date: 1994-09-06T00:00:00Z
full work available at URL: https://eudml.org/doc/155948
review text: The author considers infinite dimensional modules of the quantum group \(U_t(sl(2))\) at \(t\) a \(4r\)-th root of unity. He gives a complete classification and an explicit construction of all generic \(U_ t(sl(2))\)-modules. Recall that a \(U_t(sl(2))\)-module \(M\) is called generic if \(M\) is indecomposable, \(M\) is infinite dimensional over \(\mathbb{Q}(t)\), but \(M\) is of finite length as \(\text{End}_{U_t(sl(2))}M\)-module. There are \(2(r-1)\) non-isomorphic generic modules, and the author gives in addition an explicit description of \(\text{End}_{U_t(sl(2))}M\) for these modules.
reviewed by: Peter Littelmann
Mathematics Subject Classification ID: 17B37
zbMATH DE Number: 599665
zbMATH Keywords: quantum group \(U_t(sl(2))\)
zbMATH Keywords: infinite dimensional modules
zbMATH Keywords: generic modules
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 599665