Namespaces
Variants
Actions

User:Maximilian Janisch/latexlist/Algebraic Groups/Anisotropic kernel

From Encyclopedia of Mathematics
< User:Maximilian Janisch‎ | latexlist‎ | Algebraic Groups
Revision as of 13:36, 17 October 2019 by Maximilian Janisch (talk | contribs) (AUTOMATIC EDIT (latexlist): Replaced 18 formulas out of 18 by TEX code with an average confidence of 0.585968019082472 and a minimal confidence of 0.208.)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

This page is a copy of the article Anisotropic kernel in order to test automatic LaTeXification. This article is not my work.


The subgroup $\Omega$ of a semi-simple algebraic group $k$, defined over a field $k$, which is the commutator subgroup of the centralizer of a maximal $k$-split torus $S \subset G$; $D = [ Z _ { G } ( S ) , Z _ { G } ( S ) ]$. The anisotropic kernel $\Omega$ is a semi-simple anisotropic group defined over $k$; $D = \operatorname { rank } G -$. The concept of the anisotropic kernel plays an important role in the study of the $k$-structure of $k$ [1]. If $D = G$, i.e. if $G = 0$, then $k$ is anisotropic over $k$; if $D = ( e )$, the group $k$ is called quasi-split over $k$.

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:
Maximilian Janisch/latexlist/Algebraic Groups/Anisotropic kernel. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Maximilian_Janisch/latexlist/Algebraic_Groups/Anisotropic_kernel&oldid=43988