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

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

Author(s) -

Bernold Fiedler

Publication year - 1997

Publication title -

zeitschrift für analysis und ihre anwendungen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.567

H-Index - 35

eISSN - 1661-4534

pISSN - 0232-2064

DOI - 10.4171/zaa/756

Subject(s) - ideal (ethics) , algebra over a field , tensor (intrinsic definition) , decomposition , tensor algebra , tensor decomposition , mathematics , pure mathematics , computer science , algebra representation , cellular algebra , chemistry , philosophy , organic chemistry , epistemology

Let I be a left ideal of a group ring C[G] of a finite group C, for which a decomposition I = e;-1 Ik into minimal left ideals IA; is given. We present an algorithm, which determines a decomposition of the left ideal I . a, a E 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,.] of a symmetric group 8,., their decomposition and the reduction of tensor expressions are discussed.

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