Difference between revisions of "Quasi-split group"
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| − | <table><TR><TD valign="top">[a1]</TD> <TD valign="top"> | + | <table><TR><TD valign="top">[a1]</TD> <TD valign="top"> J.E. Humphreys, "Linear algebraic groups" , Springer (1975) pp. Sect. 35.1 {{MR|0396773}} {{ZBL|0325.20039}} </TD></TR></table> |
Revision as of 14:51, 24 March 2012
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 MR0396773 Zbl 0325.20039 |
How to Cite This Entry:
Quasi-split group. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Quasi-split_group&oldid=13662
Quasi-split group. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Quasi-split_group&oldid=13662
This article was adapted from an original article by V.L. Popov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article