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Zapiski Nauchnykh Seminarov 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
Full-text PDF (193 kB) Citations (2)
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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
Received: 23.11.2017
English version:
Journal of Mathematical Sciences (New York), 2018, Volume 232, Issue 2, Pages 121–128
DOI: https://doi.org/10.1007/s10958-018-3862-5
Bibliographic databases:
Document Type: Article
UDC: 517.54+519.217.7
Language: Russian
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{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85047408339}
Linking options:
  • https://www.mathnet.ru/eng/znsl6495
  • https://www.mathnet.ru/eng/znsl/v462/p39
    • This publication is cited in the following 2 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
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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