# A Use of Ideal Decomposition in the Computer Algebra of Tensor Expressions

### Bernold Fiedler

Freie Universität Berlin, Germany

## Abstract

Let $I$ be a left ideal of a group ring $C[G]$ of a finite group $G$, for which a decomposition $I=⊕_{k=1}I_{k}$ into minimal left ideals $I_{k}$ is given. We present an algorithm, which determines a decomposition of the left ideal $I⋅a,a∈C[G]$, 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 $C[S_{r}]$ of a symmetric group $S_{r}$, their decomposition and the reduction of tensor expressions are discussed.

## Cite this article

Bernold Fiedler, A Use of Ideal Decomposition in the Computer Algebra of Tensor Expressions. Z. Anal. Anwend. 16 (1997), no. 1, pp. 145–164

DOI 10.4171/ZAA/756