Naturally graded Lie algebras of slow growth

Abstract

Abstract A pro-nilpotent Lie algebra is said to be naturally graded if it is isomorphic to its associated graded Lie algebra with respect to the filtration by the ideals in the lower central series. Finite-dimensional naturally graded Lie algebras are known in sub-Riemannian geometry and geometric control theory, where they are called Carnot algebras. We classify the finite-dimensional and infinite-dimensional naturally graded Lie algebras with the property An arbitrary Lie algebra of this class is generated by the two- dimensional subspace , and the corresponding growth function satisfies the bound . Bibliography: 32 titles.