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arXiv · 1501.01605

Two-Step and Three-Step Nilpotent Lie Algebras Constructed from Schreier Graphs

Allie Ray
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Abstract

We associate a two-step nilpotent Lie algebra to an arbitrary Schreier graph. We then use properties of the Schreier graph to determine necessary and sufficient conditions for this Lie algebra to extend to a three-step nilpotent Lie algebra. As an application, if we start with pairs of non-isomorphic Schreier graphs coming from Gassmann-Sunada triples, we prove that the pair of associated two-step nilpotent Lie algebras are always isometric. In contrast, we use a well-known pair of Schreier graphs to show that the associated three-step nilpotent extensions need not be isometric.

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Allie Ray. 2015-01-16. Two-Step and Three-Step Nilpotent Lie Algebras Constructed from Schreier Graphs. https://arxiv.org/abs/1501.01605

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