Geometric invariants for nilpotent metric Lie algebras with applications to moduli spaces of nilsoliton metrics

Abstract

We present new tools for determining whether two nilpotent metric Lie algebras are in the same isometry class. We exhibit new examples of continuous families of nilsoliton metric Lie algebras, including deformations of uniform metric Lie algebras. We show that all algebras of generalized Heisenberg type except for Heisenberg algebras and two others admit deformations by nilsoliton metric Lie algebras.