Published Paper
Inserted: 19 jul 2021
Last Updated: 27 apr 2022
Journal: J. Geom. Phys.
Volume: 173
Pages: 104433
Year: 2022
Doi: doi.org/10.1016/j.geomphys.2021.104433
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 $\leq 7$; in dimension $8$ for corank $\leq 1$; in dimension $9$ for corank zero.