Geodesic
Two-Step and Three-Step Nilpotent Lie Algebras Constructed from Schreier Graphs
Allie Ray1
1Mathematics Department, University of Texas at Arlington, Box 19408, Arlington, TX 76019-0408, U.S.A.
Journal of Lie Theory, Tome 26 (2016) no. 2, pp. 479-495

Voir la notice de l'article provenant de la source Heldermann Verlag

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

Allie Ray  1

1 Mathematics Department, University of Texas at Arlington, Box 19408, Arlington, TX 76019-0408, U.S.A. 
Allie 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/JOLT_2016_26_2_a5/
@article{JOLT_2016_26_2_a5,
     author = {Allie 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/JOLT_2016_26_2_a5/}
}
TY  - JOUR
AU  - Allie Ray
TI  - Two-Step and Three-Step Nilpotent Lie Algebras Constructed from Schreier Graphs
JO  - Journal of Lie Theory
PY  - 2016
SP  - 479
EP  - 495
VL  - 26
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/JOLT_2016_26_2_a5/
ID  - JOLT_2016_26_2_a5
ER  - 
%0 Journal Article
%A Allie Ray
%T Two-Step and Three-Step Nilpotent Lie Algebras Constructed from Schreier Graphs
%J Journal of Lie Theory
%D 2016
%P 479-495
%V 26
%N 2
%U http://geodesic.mathdoc.fr/item/JOLT_2016_26_2_a5/
%F JOLT_2016_26_2_a5