A Use of Ideal Decomposition in the Computer Algebra of Tensor Expressions
Bernold Fiedler · Zeitschrift für Analysis und ihre Anwendungen · 1997
Let I be a left ideal of a group ring \mathbb C[G] of a finite group G , for which a decomposition I = \oplus ^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[S_r] of a symmetric group S_r , their decomposition and the reduction of tensor expressions are discussed.