Constructing matrix representations of finitely presented groups

Authors:
S. A. Linton
Affiliations:
Institut für Experimentelle Mathematik, Ellernstr. 29, D4300 Essen-12, Germany
Venue:
Journal of Symbolic Computation - Special issue on computational group theory: part 2
Year:
1991

Citing 1
Cited 2

Double coset enumeration

Journal of Symbolic Computation - Special issue on computational group theory: part 2

Constructing Irreducible Representations of Finitely Presented Algebras

Journal of Symbolic Computation
Cited References

Computer algebra handbook

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Abstract

The Todd-Coxeter coset enumeration algorithm is one of the most important tools of computational group theory. It may be viewed as a means of constructing permutation representations of finitely presented groups. In this paper we present an analogous algorithm for directly constructing matrix representations over various fields. In fact the algorithm is more general than this, and can be used to construct matrix representations of finitely generated algebras. The algorithm (with some restrictions) has been implemented as a C program and some results obtained with this implementation are described.