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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

Editorial Board: Bamberg, John / Bannai, Eiichi / Cavalieri, Renzo / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Ratcliffe, John G. / Scharlau, Rudolf / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard

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1615-7168
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Volume 14, Issue 3

Issues

On the existence of nilsolitons on 2-step nilpotent Lie groups

Univ. D. Oscari
Published Online: 2014-07-08 | DOI: https://doi.org/10.1515/advgeom-2013-0039

Abstract

A 2-step nilpotent Lie algebra n is said to be of type (p, q) if dim n = p + q and dim[n, n] = p. By considering a class of 2-step nilpotent Lie algebras naturally attached to graphs, we prove that there exist indecomposable, 2-step nilpotent Lie groups of type (p, q) which do not admit a nilsoliton metric for every pair (p, q) such that 21 ≤ q and q − 1 ≤ p ≤½ q2 − 5/2q + 9. This improves a result due to Jablonski [6].

About the article

Published Online: 2014-07-08

Published in Print: 2014-07-01


Citation Information: Advances in Geometry, Volume 14, Issue 3, Pages 483–497, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2013-0039.

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© 2014 by Walter de Gruyter Berlin/Boston.Get Permission

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