Quasi-split group

quasi-splittable group, over a field

An affine algebraic group (cf. Affine group; Algebraic group) defined over containing a Borel subgroup defined over the same field. Every affine algebraic group becomes a quasi-split group for some extension of the ground field, for example, over the algebraic closure of this field. Every affine algebraic group defined over a finite field is quasi-split over . See also Split group.

Comments

A group can be quasi-split over , or -quasi-split, without being -split.

References

[a1]	J.E. Humphreys, "Linear algebraic groups" , Springer (1975) pp. Sect. 35.1