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.
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 On,n+2, the unitary groups SUn,n and SUn,n+1, and the form of E6 with signature 2.
quasi, split, group, mathematics, quasi, split, group, over, field, reductive, group, with, borel, subgroup, defined, over, field, simply, connected, quasi, split, groups, over, field, correspond, actions, absolute, galois, group, dynkin, diagram, examples, ed. 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 editAll 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 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 On n 2 the unitary groups SUn n and SUn n 1 and the form of E6 with signature 2 References editLang Serge 1956 Algebraic groups over finite fields American Journal of Mathematics 78 555 563 doi 10 2307 2372673 ISSN 0002 9327 JSTOR 2372673 MR 0086367 Retrieved from https en wikipedia org w index php title Quasi split group amp oldid 1155321577, wikipedia, wiki, book, books, library,
