Radical of an algebraic group explained

\operatorname{GL} _{n(K)} (for a field K) is the subgroup consisting of scalar matrices, i.e. matrices (a _{ij} ) with a _{11} = ... = a _{nn} and a _{ij} =0 for i \ne j .

An algebraic group is called semisimple if its radical is trivial, i.e., consists of the identity element only. The group

\operatorname{SL} _{n(K)} 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