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arXiv · 2507.04063

On the rigidity of k-step nilpotent graph Lie algebras

Josefina Barrionuevo·Paulo Tirao
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Abstract

We thoroughly explore the class of k-step nilpotent Lie algebras associated with a simple graph looking for k-step nilpotent Lie algebras which are rigid in the variety of at most k-step nilpotent Lie algebras. We find out that, besides the complete graph, the only examples arise for k=2 and graphs of at most 4 vertices. A key tool to prove non-k-rigidity in this context, is a general construction of non-trivial deformations for naturally graded nilpotent Lie algebras.

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Josefina Barrionuevo, Paulo Tirao. 2025-07-05. On the rigidity of k-step nilpotent graph Lie algebras. https://doi.org/10.1142/s0219498827500769

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