TL;DR
This paper classifies nice nilpotent Lie algebras with nilsoliton metrics across various signatures, providing a systematic approach to determine their existence through linear and polynomial systems, especially in low dimensions.
Contribution
It offers a comprehensive classification of nice nilsolitons up to dimension 9 and reduces the existence problem to linear and polynomial equations for general signatures.
Findings
Classified nice Riemannian nilsolitons up to dimension 9.
Reduced the existence problem to linear and polynomial systems.
Provided classifications for various signatures and coranks.
Abstract
We study nice nilpotent Lie algebras admitting a diagonal nilsoliton metric. We classify nice Riemannian nilsolitons up to dimension . For general signature, we show that determining whether a nilpotent nice Lie algebra admits a nilsoliton metric reduces to a linear problem together with a system of as many polynomial equations as the corank of the root matrix. We classify nice nilsolitons of any signature: in dimension ; in dimension for corank ; in dimension for corank zero.
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