Anisotropic kernel

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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 .


[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
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Anisotropic kernel. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by V.P. Platonov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article