{{Short description|Linear algebraic group}} 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.
==Examples== 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.
{{harvtxt|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 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.
==References== *{{Citation | last1=Lang | first1=Serge | author1-link=Serge Lang | title=Algebraic groups over finite fields | jstor=2372673 |mr=0086367 | year=1956 | journal=American Journal of Mathematics | issn=0002-9327 | volume=78 | pages=555–563 | doi=10.2307/2372673}}
Category:Linear algebraic groups