The Waring problem for Lie groups and Chevalley groups

Chun Yin Hui*, Michael Larsen, Aner Shalev

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


The classical Waring problem deals with expressing every natural number as a sum of g(k) kth 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.

Original languageAmerican English
Pages (from-to)81-100
Number of pages20
JournalIsrael Journal of Mathematics
Issue number1
StatePublished - 1 Sep 2015

Bibliographical note

Publisher Copyright:
© 2015, Hebrew University of Jerusalem.


Dive into the research topics of 'The Waring problem for Lie groups and Chevalley groups'. Together they form a unique fingerprint.

Cite this