Matrix Generators for the Orthogonal Groups

Author

L. J. Rylands and D. E. Taylor

Status

Research Report 97-7
To appear in J. Symbolic Computation
Date: revised 5 March 1997

Abstract

We describe the (well known) connection between the orthogonal groups over a finite field and the Chevalley groups of type B_m, D_m and ²D_m and their Lie algebras, then give matrix generators for the derived groups of the orthogonal groups. The generators correspond to Steinberg's generators for the associated Chevalley group. These generators allow the straightforward construction of the orthogonal groups in computer algebra systems such as Magma and GAP.

Key phrases

Matrix generators, orthogonal groups, Magma, symbolic computation

AMS Subject Classification (1991)

Primary: 68Q40
Secondary: 20G40, 20-04

Content

The paper is available in the following forms:

TeX dvi format:: 1997-7.dvi.gz (19kB) or 1997-7.dvi (47kB)
PostScript:: 1997-7.ps.gz (52kB) or 1997-7.ps (178kB)

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

Sydney Mathematics and Statistics