We study nice nilpotent Lie algebras admitting a diagonal nilsoliton metric. We classify nice Riemannian nilsolitons up to dimension 9. 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 ≤7; in dimension 8 for corank ≤1; in dimension 9 for corank zero.
Conti, D., Rossi, F. (2022). Nice pseudo-Riemannian nilsolitons. JOURNAL OF GEOMETRY AND PHYSICS, 173(March 2022) [10.1016/j.geomphys.2021.104433].
Nice pseudo-Riemannian nilsolitons
Conti D.;Rossi F. A.
2022
Abstract
We study nice nilpotent Lie algebras admitting a diagonal nilsoliton metric. We classify nice Riemannian nilsolitons up to dimension 9. 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 ≤7; in dimension 8 for corank ≤1; in dimension 9 for corank zero.
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