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Quasi-split group

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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