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The Waring problem for Lie groups and Chevalley groups
- Source :
- Israel Journal of Mathematics, 210(1), 81-100. Jerusalem, Israel: Magnes Press (2015).
- Publication Year :
- 2015
- Publisher :
- Springer Science and Business Media LLC, 2015.
-
Abstract
- The classical Waring problem deals with expressing every natural number as a sum of g(k) k th powers. Similar problems were recently studied in group theory, where we aim to present group elements as short products of values of a given word w ≠ 1. In this paper we study this problem for Lie groups and Chevalley groups over infinite fields. We show that for a fixed word w ≠ 1 and for a classical connected real compact Lie group G of sufficiently large rank we have w(G)2 = G, namely every element of G is a product of 2 values of w. We prove a similar result for non-compact Lie groups of arbitrary rank, arising from Chevalley groups over ℝ or over a p-adic field. We also study this problem for Chevalley groups over arbitrary infinite fields, and show in particular that every element in such a group is a product of two squares.
- Subjects :
- Pure mathematics
Group (mathematics)
General Mathematics
Simple Lie group
010102 general mathematics
Lie group
Group Theory (math.GR)
010103 numerical & computational mathematics
01 natural sciences
Waring's problem
Group of Lie type
FOS: Mathematics
Mathematics [G03] [Physical, chemical, mathematical & earth Sciences]
Maximal torus
Mathématiques [G03] [Physique, chimie, mathématiques & sciences de la terre]
0101 mathematics
Mathematics - Group Theory
E8
Group theory
Mathematics
Subjects
Details
- ISSN :
- 15658511 and 00212172
- Volume :
- 210
- Database :
- OpenAIRE
- Journal :
- Israel Journal of Mathematics
- Accession number :
- edsair.doi.dedup.....3018072219cd370241287d95c924518d