In mathematics, a quasi-split group over a field is a reductive group with a Borel subgroup defined over the field. Simply connected quasi-split groups over a field correspond to actions of the absolute Galois group on a Dynkin diagram.
All split 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.
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 groups O<sub>n,n+2</sub>, the unitary groups SU<sub>n,n</sub> and SU<sub>n,n+1</sub>, and the form of E<sub>6</sub> with signature 2.