
Journal of Lie Theory 26 (2016), No. 2, 479495 Copyright Heldermann Verlag 2016 TwoStep and ThreeStep Nilpotent Lie Algebras Constructed from Schreier Graphs Allie Ray Mathematics Department, University of Texas at Arlington, Box 19408, Arlington, TX 760190408, U.S.A. allie.ray@mavs.uta.edu We associate a twostep 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 threestep nilpotent Lie algebra. As an application, if we start with pairs of nonisomorphic Schreier graphs coming from GassmannSunada triples, we prove that the pair of associated twostep nilpotent Lie algebras are always isometric. In contrast, we use a wellknown pair of Schreier graphs to show that the associated threestep nilpotent extensions need not be isometric. Keywords: Metric Nilpotent Lie Algebras, Schreier Graphs, GassmannSunada Triples. MSC: 05C99, 17B30, 22E25 [ Fulltextpdf (306 KB)] for subscribers only. 