# 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://www.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