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On Multicommutators for Simple Algebraic Groups

โœ Scribed by Nikolai Gordeev; Ulf Rehmann

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
158 KB
Volume
245
Category
Article
ISSN
0021-8693

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โœฆ Synopsis

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.

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