Abstract
In this work we associate a Lie algebra to every finite simple graph and obtain a necessary and sufficient condition for the existence of degenerations between these Lie algebras. As a corollary, we obtain that all these algebras belong to the irreducible component within the variety of 2-step nilpotent Lie algebras, given by the orbit closure of the free 2-step nilpotent Lie algebra.
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Correction Statement
This article has been republished with minor changes. These changes do not impact the academic content of the article.