Anisotropic kernel
From Encyclopedia of Mathematics
The subgroup of a semi-simple algebraic group
, defined over a field
, which is the commutator subgroup of the centralizer of a maximal
-split torus
;
. The anisotropic kernel
is a semi-simple anisotropic group defined over
;
. The concept of the anisotropic kernel plays an important role in the study of the
-structure of
[1]. If
, i.e. if
, then
is anisotropic over
; if
, the group
is called quasi-split over
.
References
[1] | J. Tits, "Classification of algebraic simple groups" , Algebraic Groups and Discontinuous Subgroups , Proc. Symp. Pure Math. , 9 , Amer. Math. Soc. (1966) pp. 33–62 |
[2] | A. Borel, J. Tits, "Groupes réductifs" Publ. Math. IHES , 27 (1965) pp. 55–150 MR0207712 Zbl 0145.17402 |
How to Cite This Entry:
Anisotropic kernel. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Anisotropic_kernel&oldid=21851
Anisotropic kernel. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Anisotropic_kernel&oldid=21851
This article was adapted from an original article by V.P. Platonov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article