Algorithmic construction of Chevalley bases

K. Magaard, R. A. Wilson
2012 LMS Journal of Computation and Mathematics  
AbstractWe present a new algorithm for constructing a Chevalley basis for any Chevalley Lie algebra over a finite field. This is a necessary component for some constructive recognition algorithms of exceptional quasisimple groups of Lie type. When applied to a simple Chevalley Lie algebra in characteristicp⩾5, our algorithm has complexity involving the seventh power of the Lie rank, which is likely to be close to best possible.
doi:10.1112/s1461157012001180 fatcat:wttxkvgksnb2vjn4lz5pjs3vti