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Izv. RAN. Ser. Mat., 2011, Volume 75, Issue 2, Pages 19–34 (Mi izv4205)  

This article is cited in 4 scientific papers (total in 4 papers)

The amenability of the substitution group of formal power series

I. K. Babenkoa, S. A. Bogatyib

a Institut de Mathématiques et de Modélisation de Montpellier
b M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: We study the amenability property for the group $\mathcal{J}(\mathbf{k})$ of formal power series in one variable with coefficients in a commutative ring $\mathbf{k}$ with identity. We show that there exists an invariant mean on the space $C_{\mathrm{u}}^*(\mathcal{J}(\mathbf{k}))$ of uniformly continuous bounded functions on this group. This is equivalent to the fact that every continuous action of $\mathcal{J}(\mathbf{k})$ on every compact space has an invariant probability measure.

Keywords: topological group, group action, invariant mean.

DOI: https://doi.org/10.4213/im4205

Full text: PDF file (543 kB)
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English version:
Izvestiya: Mathematics, 2011, 75:2, 239–252

Bibliographic databases:

Document Type: Article
UDC: 512.546+517.987.5
MSC: 20E18, 22A10, 43A07, 46E15
Received: 20.02.2009
Revised: 04.03.2010

Citation: I. K. Babenko, S. A. Bogatyi, “The amenability of the substitution group of formal power series”, Izv. RAN. Ser. Mat., 75:2 (2011), 19–34; Izv. Math., 75:2 (2011), 239–252

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. M. Buchstaber, “Complex cobordism and formal groups”, Russian Math. Surveys, 67:5 (2012), 891–950  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. I. K. Babenko, “Algebra, geometry, and topology of the substitution group of formal power series”, Russian Math. Surveys, 68:1 (2013), 1–68  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. Barroso C.S., Mbombo B.R., Pestov V.G., “On Topological Groups With An Approximate Fixed Point Property”, An. Acad. Bras. Cienc., 89:1 (2017), 19–30  crossref  mathscinet  zmath  isi  scopus
    4. Grigorchuk R., de la Harpe P., “Amenability and Ergodic Properties of Topological Groups: From Bogolyubov Onwards”, Groups, Graphs and Random Walks, London Mathematical Society Lecture Note Series, 436, eds. CeccheriniSilberstein T., Salvatori M., SavaHuss E., Cambridge Univ Press, 2017, 215–249  mathscinet  zmath  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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