Let $B$ be the algebraic group of upper triangular matrices with entires in some algebraically closed field. I would like to know what is the radical of this group is… Any explanation would be appreciated. thanks you.
The radical of upper triangular matrices
abstract-algebraalgebraic-geometryalgebraic-groupsgroup-theorylinear algebra
Best Answer
The unipotent radical of the group $B_n(K)$, which is the standard Borel subgroup of $GL_n(K)$, consists of unitriangular uppertriagular matrices, i.e., with all diagonal elements equal to $1$. The (solvable) radical of $B_n(K)$ equals $B_n(K)$ itself, since the Borel subgroup is solvable.