We construct a faithful self-similar action of the discrete Heisenberg group with the following properties: This action is self-replicating, finite-state, level-transitive, and noncontracting. Moreover, there exist orbital Schreier graphs of action on the boundary of the tree with different degrees of growth.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, No. 11, pp. 1456–1462, November, 2013.
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Bondarenko, I., Kravchenko, R. Schreier Graphs for a Self-Similar Action of the Heisenberg Group. Ukr Math J 65, 1612–1618 (2014). https://doi.org/10.1007/s11253-014-0883-1
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DOI: https://doi.org/10.1007/s11253-014-0883-1