A Lie group is a group with the structure of a manifold. Therefore, discrete groups do not count. However, the most useful Lie groups are defined as subgroups of some matrix group. The analogous subgroups where the matrices are taken to be over a finite field (but the group is defined in the same way) are called the Lie-type groups. They are a kind of linear algebraic group.

The Lie-type groups include the Chevalley groups (i.e., , , , ), twisted Chevalley groups, and the Tits group.

Portions of this entry contributed by John Renze

Wilson, R. A. "ATLAS of Finite Group Representation." http://for.mat.bham.ac.uk/atlas/html/contents.html#lie.

CITE THIS AS:

Renze, John and Weisstein, Eric W. "Lie-Type Group." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Lie-TypeGroup.html