Matrix Generators for Exceptional Groups of Lie Type


R. B. Howlett, L. J. Rylands and D. E. Taylor


Research Report 99-14
Date: 24 June 1999


This paper gives a uniform method of constructing generators for finite groups of Lie type with particular emphasis on the exceptional groups. The algorithm constructs matrices for the action of root elements on the lowest dimensional representation of an associated Lie algebra. These generators have been implemented in the computer algebra system Magma and this completes the provision of pairs of matrix generators for all finite groups of Lie type.

Key phrases

exceptional Lie group. Chevalley group. computational algebra.

AMS Subject Classification (1991)

Primary: 20C40
Secondary: 20F05, 17B25


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