On the dimension of capable Lie algebras of class two

Abstract

‎Let $ L $ be a finite-dimensional nilpotent Lie algebra of class two over a field $\mathbb{F} $ of characteristic different from two‎. ‎This talk gives an upper bound for the dimension of capable nilpotent Lie algebras of class two‎. ‎Moreover‎, ‎the exact structure of Schur multiplier for each non-capable generalized Heisenberg Lie algebras of rank $3$ is determined‎.