RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Mat. Sb.: Year: Volume: Issue: Page: Find

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

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.

Full text: PDF file (1019 kB)
References: PDF file   HTML file

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

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} 

• http://mi.mathnet.ru/eng/msb2779
• http://mi.mathnet.ru/eng/msb/v155/i1/p81

 SHARE:

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
2. Hirai T., “Irreducible Unitary Representations of the Group of Diffeomorphisms of a Noncompact Manifold”, J. Math. Kyoto Univ., 33:3 (1993), 827–864
3. Shimomura H., “1-Cocycles on the Group of Diffeomorphisms”, J. Math. Kyoto Univ., 38:4 (1998), 695–725
4. Shimomura H., “1-Cocycles on the Group of Diffeomorphisms II”, J. Math. Kyoto Univ., 39:3 (1999), 493–527
•  Number of views: This page: 227 Full text: 61 References: 46 First page: 3