%0 Journal Article
%T Generic properties of 2-step nilpotent Lie algebras and torsion-free groups
%A Maria V. Milentyeva
%J Mathematics
%D 2014
%I arXiv
%X To define the notion of a generic property of finite dimensional 2-step nilpotent Lie algebras we use standard correspondence between such Lie algebras and points of an appropriate algebraic variety, where a negligible set is one contained in a proper Zariski-closed subset. We compute the maximal dimension of an abelian subalgebra of a generic Lie algebra and give a sufficient condition for a generic Lie algebra to admit no surjective homomorphism onto a non-abelian Lie algebra of a given dimension. Also we consider analogous questions for finitely generated torsion free nilpotent groups of class 2.
%U http://arxiv.org/abs/1408.0871v1