# Quasi-split group

From Encyclopedia of Mathematics

*quasi-splittable group, over a field $k$*

An affine algebraic group (cf. Affine group; Algebraic group) defined over $k$ 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 $k$ is quasi-split over $k$. See also Split group.

#### Comments

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

#### References

[a1] | J.E. Humphreys, "Linear algebraic groups" , Springer (1975) pp. Sect. 35.1 MR0396773 Zbl 0325.20039 |

**How to Cite This Entry:**

Quasi-split group.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Quasi-split_group&oldid=32385

This article was adapted from an original article by V.L. Popov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article