JournalszaaVol. 16, No. 1pp. 145–164

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

  • Bernold Fiedler

    Freie Universität Berlin, Germany
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Abstract

Let II be a left ideal of a group ring C[G]\mathbb C[G] of a finite group GG, for which a decomposition I=k=1mIkI = \oplus ^m_{k=1} I_k into minimal left ideals IkI_k is given. We present an algorithm, which determines a decomposition of the left ideal Ia,aC[G]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 C[Sr]\mathbb C[S_r] of a symmetric group SrS_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