A use of ideal decomposition in the computer algebra of tensor expressions
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.
scientific article; zbMATH DE number 1011107
scientific article