# Matrix Generators for Exceptional Groups of Lie Type

## Author

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

## Status

Research Report 99-14

Date: 24 June 1999

## Abstract

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

## Content

The paper is available in the following forms:
- TeX dvi format:
- 1999-14.dvi.gz (31kB) or
1999-14.dvi (83kB)

- PostScript:
- 1999-14.ps.gz (75kB) or
1999-14.ps (262kB)

##### To minimize network load, please choose the smaller gzipped .gz form if
and only if your browser client supports it.

Sydney Mathematics and Statistics