Graphs and two-step nilpotent Lie algebras (Q2347645)

If \(k\) is a field with characteristic not equal to 2, then a non-abelian finite dimensional Lie algebra \(n\) over \(k\) is said to be two-step nilpotent Lie algebra if \([n,[n,n]]=\{0\}\). In this paper the author uses a well-known method, associating be a two-step nilpotent Lie algebra with a finite simple graph. Also, he proves that the two-step nilpotent Lie algebras associated with two graphs are Lie isomorphic if and only if the graphs from which they arise are isomorphic.