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Singular foliation $ C\sp *$-algebras

Author: Albert Jeu-Liang Sheu
Journal: Proc. Amer. Math. Soc. 104 (1988), 1197-1203
MSC: Primary 46L55; Secondary 22D25, 22E46, 57R30
MathSciNet review: 930243
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Abstract: A way to construct $ {C^*}$-algebras from the so-called singular foliations is proposed, which generalizes Connes' construction of $ {C^*}$-algebras of regular foliations. A certain desired property is shown to hold for such $ {C^*}$-algebras and some connection with the boundary behavior of pseudodifferential operators is indicated.

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  • [Bou] Louis Boutet de Monvel, Boundary problems for pseudo-differential operators, Acta Math. 126 (1971), no. 1-2, 11–51. MR 0407904
  • [Con] A. Connes, A survey of foliations and operator algebras, Operator algebras and applications, Part I (Kingston, Ont., 1980) Proc. Sympos. Pure Math., vol. 38, Amer. Math. Soc., Providence, R.I., 1982, pp. 521–628. MR 679730
  • [Daz] Pierre Dazord, Holonomie des feuilletages singuliers, C. R. Acad. Sci. Paris Sér. I Math. 298 (1984), no. 2, 27–30 (French, with English summary). MR 740083
  • [Eec] Paul Ver Eecke, Sur le groupe fondamental d’un feuilletage singulier, C. R. Acad. Sci. Paris Sér. I Math. 301 (1985), no. 18, 837–840 (French, with English summary). MR 822844
  • [Ehr] C. Ehresmann, Structures feuilletées, Proc. 5th Canad. Math. Congress, 1961, pp. 109-172.
  • [Kir] A. A. Kirillov, Unitary representations of nilpotent Lie groups, Uspehi Mat. Nauk 17 (1962), no. 4 (106), 57–110 (Russian). MR 0142001
  • [Ren] Jean Renault, A groupoid approach to 𝐶*-algebras, Lecture Notes in Mathematics, vol. 793, Springer, Berlin, 1980. MR 584266
  • [Sheu] Albert Jeu-Liang Sheu, A cancellation theorem for modules over the group 𝐶*-algebras of certain nilpotent Lie groups, Canad. J. Math. 39 (1987), no. 2, 365–427. MR 899843, 10.4153/CJM-1987-018-7
  • [Wein] Alan Weinstein, The local structure of Poisson manifolds, J. Differential Geom. 18 (1983), no. 3, 523–557. MR 723816
  • [Upm] Harald Upmeier, Index theory for multivariable Wiener-Hopf operators, J. Reine Angew. Math. 384 (1988), 57–79. MR 929978, 10.1515/crll.1988.384.57

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Article copyright: © Copyright 1988 American Mathematical Society