In mathematics, aquasi-split group over afield is areductive group with aBorel subgroup defined over the field.Simply connected quasi-split groups over a field correspond to actions of the absoluteGalois group on aDynkin diagram.
Allsplit groups (those with a split maximal torus) are quasi-split. These correspond to quasi-split groups where the action of the Galois group on the Dynkin diagram is trivial.
Lang (1956) showed that all simple algebraic groups over finite fields are quasi-split.
Over the real numbers, the quasi-split groups include the split groups and the complex groups, together with the orthogonal groupsOn,n+2, the unitary groupsSUn,n andSUn,n+1, and the form ofE6 with signature 2.