Geodesic
Two-Step and Three-Step Nilpotent Lie Algebras Constructed from Schreier Graphs
Journal of Lie theory, Tome 26 (2016) no. 2, pp. 479-495
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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.
Classification : 05C99, 17B30, 22E25
Mots-clés : Metric Nilpotent Lie Algebras, Schreier Graphs, Gassmann-Sunada Triples 
@article{JLT_2016_26_2_JLT_2016_26_2_a5,
     author = {A. Ray},
     title = {Two-Step and {Three-Step} {Nilpotent} {Lie} {Algebras} {Constructed} from {Schreier} {Graphs}},
     journal = {Journal of Lie theory},
     pages = {479--495},
     year = {2016},
     volume = {26},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JLT_2016_26_2_JLT_2016_26_2_a5/}
}
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A. Ray. Two-Step and Three-Step Nilpotent Lie Algebras Constructed from Schreier Graphs. Journal of Lie theory, Tome 26 (2016) no. 2, pp. 479-495. http://geodesic.mathdoc.fr/item/JLT_2016_26_2_JLT_2016_26_2_a5/