Radical of an algebraic group
The radical of an algebraic group is the identity component of its maximal normal solvable subgroup. For example, the radical of the general linear group (for a field K) is the subgroup consisting of
scalar matrices
, i.e. matrices with and for .
An
semisimple
if its radical is trivial, i.e., consists of the identity element only. The group is semi-simple, for example.
The subgroup of unipotent elements in the radical is called the
unipotent radical, it serves to define reductive groups
.
See also
- Reductive group
- Unipotent group
References
- "Radical of a group", Encyclopaedia of Mathematics