On the dimensions of commutative subalgebras and subgroups of nilpotent algebras and Lie groups of class 2

Abstract

We obtain the functions that bound the dimensions of finite dimensional nilpotent associative or Lie algebras of class 2 over an algebraically closed field in terms of the dimensions of their commutative subalgebras. As a result, we also compute a similar function for complex nilpotent Lie groups of class 2.