Modules over \(\mathfrak U_ q(\mathfrak s\mathfrak l_ 2)\)
type: Item
instance of: scholarly article
title: Modules over \(\mathfrak U_ q(\mathfrak s\mathfrak l_ 2)\)
zbMATH Open document ID: 0851.17015
DOI: 10.1007/BF02102012
author: Ruedi Suter
published in: Communications in Mathematical Physics
publication date: 1994-08-10T00:00:00Z
review text: The author is interested in the decomposition of tensor products of simple modules of the restricted quantum universal enveloping algebra \({\mathfrak U}_q (\mathfrak {sl}_2)\); the aim is to understand the structure of the corresponding fusion rule algebra. As a first step in his new approach, the author describes a canonical decomposition of \({\mathfrak U}_q (\mathfrak {sl}_2)\) into PIMs. A decomposition of \({\mathfrak U}_q (\mathfrak {sl}_2)\) into indecomposable left ideals is in general not unique, but the author defines a ``nice'' gradation such that the corresponding decomposition is homogeneous. This condition makes it unique. The author uses these indecomposable left ideals to determine the direct summands which occur in the tensor product of two simple \({\mathfrak U}_q (\mathfrak {sl}_2)\)-modules. In addition, the author classifies the indecomposable finite-dimensional \({\mathfrak U}_q (\mathfrak {sl}_2)\)-modules.
reviewed by: Peter Littelmann
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 16W30
zbMATH DE Number: 617391
zbMATH Keywords: decomposition
zbMATH Keywords: simple modules
zbMATH Keywords: restricted quantum universal enveloping algebra
zbMATH Keywords: fusion rule algebra
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 617391