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Zap. Nauchn. Sem. POMI, 2015, Volume 436, Pages 189–198 (Mi znsl6167)  

This article is cited in 1 scientific paper (total in 1 paper)

Several remarks on groups of automorphisms of free groups

Yu. A. Neretinabcd

a State Scientific Center of the Russian Federation - Institute for Theoretical and Experimental Physics, Moscow, Russia
b Lomonosov Moscow State University, Moscow, Russia
c Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow, Russia
d University of Vienna, Vienna, Austria

Abstract: Let $\mathbb G$ be the group of automorphisms of a free group $F_\infty$ of infinite order. Let $\mathbb H$ be the stabilizer of the first $m$ generators of $F_\infty$. We show that the double cosets $\Gamma_m=\mathbb{H\setminus G/H}$ admit a natural semigroup structure. For any compact group $K$, the semigroup $\Gamma_m$ acts in the space $L^2$ on the product of $m$ copies of $K$.

Key words and phrases: free group, infinite symmetric group, double cosets, conjugacy classes, infinite-dimensional groups.

Funding Agency Grant Number
Austrian Science Fund P22122
P25142


Full text: PDF file (184 kB)
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English version:
Journal of Mathematical Sciences (New York), 2016, 215:6, 748–754

Bibliographic databases:

UDC: 512.544.43+512.547.4
Received: 22.07.2015

Citation: Yu. A. Neretin, “Several remarks on groups of automorphisms of free groups”, Representation theory, dynamical systems, combinatorial methods. Part XXV, Zap. Nauchn. Sem. POMI, 436, POMI, St. Petersburg, 2015, 189–198; J. Math. Sci. (N. Y.), 215:6 (2016), 748–754

Citation in format AMSBIB
\Bibitem{Ner15}
\by Yu.~A.~Neretin
\paper Several remarks on groups of automorphisms of free groups
\inbook Representation theory, dynamical systems, combinatorial methods. Part~XXV
\serial Zap. Nauchn. Sem. POMI
\yr 2015
\vol 436
\pages 189--198
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6167}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3498193}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2016
\vol 215
\issue 6
\pages 748--754
\crossref{https://doi.org/10.1007/s10958-016-2880-4}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84966559711}


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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. P. Gonzalez Pagotto, “A product of double cosets of $B_\infty$”, SIGMA, 14 (2018), 134, 18 pp.  mathnet  crossref
  • Записки научных семинаров ПОМИ
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