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arXiv · 2311.12469

A Hilbert--Mumford criterion for nilsolitons

Yoshinori Hashimoto
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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.

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Yoshinori Hashimoto. 2023-11-21. A Hilbert--Mumford criterion for nilsolitons. https://arxiv.org/abs/2311.12469

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