On the existence of nilsolitons on 2-step nilpotent Lie groups

Abstract

Abstract A 2-step nilpotent Lie algebra n is said to be of type (p, q) if dim n = p + q and dim[n, n] = p. By considering a class of 2-step nilpotent Lie algebras naturally attached to graphs, we prove that there exist indecomposable, 2-step nilpotent Lie groups of type (p, q) which do not admit a nilsoliton metric for every pair (p, q) such that 21 ≤ q and q − 1 ≤ p ≤½ q2 − 5/2q + 9. This improves a result due to Jablonski [6].