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Zap. Nauchn. Sem. POMI, 2017, Volume 462, Pages 39–51 (Mi znsl6495)  

This article is cited in 2 scientific papers (total in 2 papers)

Infinite geodesics in the discrete Heisenberg group

A. M. Vershikabc, A. V. Malyutinab

a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia
b St. Petersburg State University, St. Petersburg, Russia
c Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow, Russia

Abstract: We give an exhaustive description of the family of infinite geodesics in the discrete Heisenberg group (with respect to the standard generating set). The classification of infinite geodesics is needed to describe the so-called absolute (exit boundary) of a group. The absolute of the discrete Heisenberg group will be described in a forthcoming paper.

Key words and phrases: discrete Heisenberg group, normal form, absolute, exit-boundary, geodesic.

Funding Agency Grant Number
Russian Science Foundation 17-71-20153


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English version:
Journal of Mathematical Sciences (New York), 2018, 232:2, 121–128

UDC: 517.54+519.217.7
Received: 23.11.2017

Citation: A. M. Vershik, A. V. Malyutin, “Infinite geodesics in the discrete Heisenberg group”, Representation theory, dynamical systems, combinatorial methods. Part XXVIII, Zap. Nauchn. Sem. POMI, 462, POMI, St. Petersburg, 2017, 39–51; J. Math. Sci. (N. Y.), 232:2 (2018), 121–128

Citation in format AMSBIB
\Bibitem{VerMal17}
\by A.~M.~Vershik, A.~V.~Malyutin
\paper Infinite geodesics in the discrete Heisenberg group
\inbook Representation theory, dynamical systems, combinatorial methods. Part~XXVIII
\serial Zap. Nauchn. Sem. POMI
\yr 2017
\vol 462
\pages 39--51
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6495}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2018
\vol 232
\issue 2
\pages 121--128
\crossref{https://doi.org/10.1007/s10958-018-3862-5}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85047408339}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. M. Vershik, A. V. Malyutin, “The Absolute of Finitely Generated Groups: II. The Laplacian and Degenerate Parts”, Funct. Anal. Appl., 52:3 (2018), 163–177  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. A. M. Vershik, A. V. Malyutin, “Asymptotic behavior of the number of geodesics in the discrete Heisenberg group”, J. Math. Sci. (N. Y.), 240:5 (2019), 525–534  mathnet  crossref
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