On Multicommutators for Simple Algebraic Groups

Gordeev N, Rehmann U (2001)
Journal of Algebra 245(1): 275-296.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Gordeev, N; Rehmann, UlfUniBi
Abstract / Bemerkung
There are several examples of groups for which any pair of commutators can be written such that both of them have a common entry, and one can look for a similar property for n-tuples of commutators. Here we answer, for simple algebraic groups over any field, the weaker question, under which condition the set of n-tuples of commutators with one common entry is Zariski dense in the set of all n-tuples of commutators. Surprisingly, there is a uniform bound on n in terms of the so-called Coxeter number of G to answer the question positively. An analogue result is proved for Lie algebras of simple and simply connected algebraic groups. (C) 2001 Academic Press.
Stichworte
commutators; groups; simple algebraic groups
Erscheinungsjahr
2001
Zeitschriftentitel
Journal of Algebra
Band
245
Ausgabe
1
Seite(n)
275-296
ISSN
0021-8693
Page URI
https://pub.uni-bielefeld.de/record/1615863

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Gordeev N, Rehmann U. On Multicommutators for Simple Algebraic Groups. Journal of Algebra. 2001;245(1):275-296.
Gordeev, N., & Rehmann, U. (2001). On Multicommutators for Simple Algebraic Groups. Journal of Algebra, 245(1), 275-296. https://doi.org/10.1006/jabr.2001.8929
Gordeev, N., and Rehmann, U. (2001). On Multicommutators for Simple Algebraic Groups. Journal of Algebra 245, 275-296.
Gordeev, N., & Rehmann, U., 2001. On Multicommutators for Simple Algebraic Groups. Journal of Algebra, 245(1), p 275-296.
N. Gordeev and U. Rehmann, “On Multicommutators for Simple Algebraic Groups”, Journal of Algebra, vol. 245, 2001, pp. 275-296.
Gordeev, N., Rehmann, U.: On Multicommutators for Simple Algebraic Groups. Journal of Algebra. 245, 275-296 (2001).
Gordeev, N, and Rehmann, Ulf. “On Multicommutators for Simple Algebraic Groups”. Journal of Algebra 245.1 (2001): 275-296.

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