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Difference between revisions of "Anisotropic kernel"

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<table><TR><TD valign="top">[1]</TD> <TD valign="top">  J. Tits,  "Classification of algebraic simple groups" , ''Algebraic Groups and Discontinuous Subgroups'' , ''Proc. Symp. Pure Math.'' , '''9''' , Amer. Math. Soc.  (1966)  pp. 33–62</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top">  A. Borel,  J. Tits,  "Groupes réductifs"  ''Publ. Math. IHES'' , '''27'''  (1965)  pp. 55–150</TD></TR></table>
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<table><TR><TD valign="top">[1]</TD> <TD valign="top">  J. Tits,  "Classification of algebraic simple groups" , ''Algebraic Groups and Discontinuous Subgroups'' , ''Proc. Symp. Pure Math.'' , '''9''' , Amer. Math. Soc.  (1966)  pp. 33–62 {{MR|}} {{ZBL|}} </TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top">  A. Borel,  J. Tits,  "Groupes réductifs"  ''Publ. Math. IHES'' , '''27'''  (1965)  pp. 55–150 {{MR|0207712}} {{ZBL|0145.17402}} </TD></TR></table>

Revision as of 10:02, 24 March 2012

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=21814
This article was adapted from an original article by V.P. Platonov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article