Let be a left ideal of a group ring of a finite group , for which a decomposition into minimal left ideals is given. We present an algorithm, which determines a decomposition of the left ideal , 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 of a symmetric group , 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. 145–164DOI 10.4171/ZAA/756