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Lie-Type Group


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., PSL(n,q), PSU(n,q), PSp(2n,q), POmega^epsilon(n,q)), twisted Chevalley groups, and the Tits group.


See also

Chevalley Groups, Finite Group, Lie Group, Linear Group, Orthogonal Group, Simple Group, Symplectic Group, Tits Group, Twisted Chevalley Groups, Unitary Group

Portions of this entry contributed by John Renze

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References

Wilson, R. A. "ATLAS of Finite Group Representation." http://brauer.maths.qmul.ac.uk/Atlas/v3/exc/.

Referenced on Wolfram|Alpha

Lie-Type Group

Cite this as:

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

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