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Article: The Waring problem for Lie groups and Chevalley groups
Title | The Waring problem for Lie groups and Chevalley groups |
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Authors | |
Issue Date | 2015 |
Citation | Israel Journal of Mathematics, 2015, v. 210, n. 1, p. 81-100 How to Cite? |
Abstract | © 2015, Hebrew University of Jerusalem. 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. |
Persistent Identifier | http://hdl.handle.net/10722/297342 |
ISSN | 2023 Impact Factor: 0.8 2023 SCImago Journal Rankings: 0.943 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Hui, Chun Yin | - |
dc.contributor.author | Larsen, Michael | - |
dc.contributor.author | Shalev, Aner | - |
dc.date.accessioned | 2021-03-15T07:33:33Z | - |
dc.date.available | 2021-03-15T07:33:33Z | - |
dc.date.issued | 2015 | - |
dc.identifier.citation | Israel Journal of Mathematics, 2015, v. 210, n. 1, p. 81-100 | - |
dc.identifier.issn | 0021-2172 | - |
dc.identifier.uri | http://hdl.handle.net/10722/297342 | - |
dc.description.abstract | © 2015, Hebrew University of Jerusalem. 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. | - |
dc.language | eng | - |
dc.relation.ispartof | Israel Journal of Mathematics | - |
dc.title | The Waring problem for Lie groups and Chevalley groups | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1007/s11856-015-1246-9 | - |
dc.identifier.scopus | eid_2-s2.0-84945907184 | - |
dc.identifier.volume | 210 | - |
dc.identifier.issue | 1 | - |
dc.identifier.spage | 81 | - |
dc.identifier.epage | 100 | - |
dc.identifier.eissn | 1565-8511 | - |
dc.identifier.isi | WOS:000364227000004 | - |
dc.identifier.issnl | 0021-2172 | - |