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Mat. Sb. (N.S.), 1980, Volume 113(155), Number 1(9), Pages 81–97 (Mi msb2779)  

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

Imbedding of a group of measure-preserving diffeomorphisms into a semidirect product and its unitary representations

R. S. Ismagilov


Abstract: The author considers the group $D^0(X,v)$ of diffeomorphisms of a compact manifold $X$ that preserve a measure $v$, and describes its unitary representations whose restrictions to any subgroup $D^0(Y,v)$, where $Y\simeq\mathbf R^n$, are continuous on $D^0(Y,v)$ with respect to convergence in measure in $D^0(Y,v)$. As an example, a family of representations $T^\alpha$ indexed by the nonzero elements $\alpha\in H^1(X,\mathbf R)$ is studied.
Bibliography: 12 titles.

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English version:
Mathematics of the USSR-Sbornik, 1982, 41:1, 67–81

Bibliographic databases:

UDC: 513.836
MSC: Primary 57S05, 58C35; Secondary 22E65, 58D05, 81C40
Received: 05.09.1979

Citation: R. S. Ismagilov, “Imbedding of a group of measure-preserving diffeomorphisms into a semidirect product and its unitary representations”, Mat. Sb. (N.S.), 113(155):1(9) (1980), 81–97; Math. USSR-Sb., 41:1 (1982), 67–81

Citation in format AMSBIB
\Bibitem{Ism80}
\by R.~S.~Ismagilov
\paper Imbedding of a~group of measure-preserving diffeomorphisms into a~semidirect product and its unitary representations
\jour Mat. Sb. (N.S.)
\yr 1980
\vol 113(155)
\issue 1(9)
\pages 81--97
\mathnet{http://mi.mathnet.ru/msb2779}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=590539}
\zmath{https://zbmath.org/?q=an:0484.58011|0443.58012}
\transl
\jour Math. USSR-Sb.
\yr 1982
\vol 41
\issue 1
\pages 67--81
\crossref{https://doi.org/10.1070/SM1982v041n01ABEH002221}


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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. R. S. Ismagilov, “Spherical functions on the group of diffeomorphisms preserving the volume”, Funct. Anal. Appl., 25:2 (1991), 150–152  mathnet  crossref  mathscinet  zmath  isi
    2. Hirai T., “Irreducible Unitary Representations of the Group of Diffeomorphisms of a Noncompact Manifold”, J. Math. Kyoto Univ., 33:3 (1993), 827–864  mathscinet  zmath  isi
    3. Shimomura H., “1-Cocycles on the Group of Diffeomorphisms”, J. Math. Kyoto Univ., 38:4 (1998), 695–725  mathscinet  zmath  isi
    4. Shimomura H., “1-Cocycles on the Group of Diffeomorphisms II”, J. Math. Kyoto Univ., 39:3 (1999), 493–527  mathscinet  zmath  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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