A Hilbert–Mumford criterion for nilsolitons

Transactions of the American Mathematical Society 2026 Open access

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Authors: Yoshinori Hashimoto
DOI: 10.1090/tran/9665
Cited by: 0

Abstract

We give an algebraic criterion for a nilpotent real Lie algebra and prove that it provides a necessary and sufficient condition for the associated nilpotent Lie group to admit left-invariant Ricci solitons, called nilsolitons. As an application of this result, we generalise Nikolayevsky’s criterion for the existence of nilsolitons to nilpotent Lie algebras without nice bases. We further prove a modified version of the Taketomi–Tamaru conjecture for nilpotent Lie groups which gives an obstruction to the existence of nilsolitons.

Fields of Study & Subjects

Advanced Topics in Algebra Algebraic structures and combinatorial models Nonlinear Waves and Solitons

Publication details

Journal / source
Transactions of the American Mathematical Society
Volume
379
Issue
9
Pages
6589–6612
Publication date
15 June 2026
Language
EN