A short note on 2-step nilpotent Lie algebras associated with graphs

Abstract

In this note we consider 2-step nilpotent Lie algebras associated with graphs. We prove that 2-step nilpotent Lie algebras $\n$ and $\n'$ associated with graphs $(S,E)$ and $(S^{\prime },E^{\prime })$ respectively are isomorphic if and only if $(S,E)$ and $(S^{\prime },E^{\prime })$ are isomorphic.

This paper has been withdrawn by the author due to some mistakes in proof of the main theorem. The correct version (with different title) will be uploaded soon