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
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.
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Mathematics of the USSR-Sbornik, 1982, 41:1, 67–81
MSC: Primary 57S05, 58C35; Secondary 22E65, 58D05, 81C40
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
\paper Imbedding of a~group of measure-preserving diffeomorphisms into a~semidirect product and its unitary representations
\jour Mat. Sb. (N.S.)
\jour Math. USSR-Sb.
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R. S. Ismagilov, “Spherical functions on the group of diffeomorphisms preserving the volume”, Funct. Anal. Appl., 25:2 (1991), 150–152
Hirai T., “Irreducible Unitary Representations of the Group of Diffeomorphisms of a Noncompact Manifold”, J. Math. Kyoto Univ., 33:3 (1993), 827–864
Shimomura H., “1-Cocycles on the Group of Diffeomorphisms”, J. Math. Kyoto Univ., 38:4 (1998), 695–725
Shimomura H., “1-Cocycles on the Group of Diffeomorphisms II”, J. Math. Kyoto Univ., 39:3 (1999), 493–527
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