A use of ideal decomposition in the computer algebra of tensor expressions
type: Item
instance of: scholarly article
title: A use of ideal decomposition in the computer algebra of tensor expressions
zbMATH Open document ID: 0872.20017
DOI: 10.4171/ZAA/756
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1997-10-13T00:00:00Z
review text: Summary: Let \(I\) be a left ideal of a group ring \(\mathbb{C}[G]\) of a finite group \(G\), for which a decomposition \(I=\bigoplus^m_{k=1}I_k\) into minimal left ideals \(I_k\) is given. We present an algorithm, which determines a decomposition of the left ideal \(I\cdot a\), \(a\in\mathbb{C}[G]\), into minimal left ideals and a corresponding set of primitive orthogonal idempotents by means of a computer. The algorithm is motivated by the computer algebra of tensor expressions. Several aspects of the connection between left ideals of the group ring \(\mathbb{C}[{\mathcal S}_r]\) of a symmetric group \({\mathcal S}_r\), their decomposition and the reduction of tensor expressions are discussed.
Mathematics Subject Classification ID: 20C40
Mathematics Subject Classification ID: 20C30
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 16D25
zbMATH DE Number: 1011107
zbMATH Keywords: group rings
zbMATH Keywords: finite groups
zbMATH Keywords: minimal left ideals
zbMATH Keywords: primitive orthogonal idempotents
zbMATH Keywords: computer algebra
zbMATH Keywords: tensor expressions
author: Bernd Fiedler
describes a project that uses: ATENSOR
describes a project that uses: SCHUR
describes a project that uses: Ricci
describes a project that uses: MathTensor
describes a project that uses: GRTensorII
describes a project that uses: SYMMETRICA
describes a project that uses: Redten
MaRDI profile type: Publication
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cites work: Q5772226
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description: scientific article; zbMATH DE number 1011107