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

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