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2011 | 9 | 4 | 833-850
Tytuł artykułu

On the index of nonlocal elliptic operators for compact Lie groups

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Treść / Zawartość
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Języki publikacji
EN
Abstrakty
EN
We consider a class of nonlocal operators associated with a compact Lie group G acting on a smooth manifold. A notion of symbol of such operators is introduced and an index formula for elliptic elements is obtained. The symbol in this situation is an element of a noncommutative algebra (crossed product by G) and to obtain an index formula, we define the Chern character for this algebra in the framework of noncommutative geometry.
Wydawca
Czasopismo
Rocznik
Tom
9
Numer
4
Strony
833-850
Opis fizyczny
Daty
wydano
2011-08-01
online
2011-05-26
Bibliografia
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  • [10] Connes A., Cyclic cohomology and the transverse fundamental class of a foliation, In: Geometric Methods in Operator Algebras, Kyoto, 1983, Pitman Res. Notes Math. Ser., 123, Longman, Harlow, 1986, 52–144
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  • [17] Koszul J.L., Sur certains groupes de transformations de Lie, In: Géométrie Différentielle, Colloques Internationaux du Centre National de la Recherche Scientifique, Strasbourg, 1953, Centre National de la Recherche Scientifique, Paris, 1953, 137–141
  • [18] Nazaikinskii V.E., Savin A.Yu., Sternin B.Yu., Elliptic Theory and Noncommutative Geometry, Oper. Theory Adv. Appl., 183, Birkhäuser, Basel, 2008
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  • [20] Pedersen G.K., C*-Algebras and Their Automorphism Groups, London Math. Soc. Monogr., 14, Academic Press, London-New York, 1979
  • [21] Quillen D., Superconnections and the Chern character, Topology, 1985, 24(1), 89–95 http://dx.doi.org/10.1016/0040-9383(85)90047-3
  • [22] Sternin B.Yu., On a class of nonlocal elliptic operators for compact Lie groups. Uniformization and finiteness theorem, Cent. Eur. J. Math., 2011, 9(4)
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  • [24] Vergne M., Equivariant index formulas for orbifolds, Duke Math. J., 1996, 82(3), 637–652 http://dx.doi.org/10.1215/S0012-7094-96-08226-5
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Typ dokumentu
Bibliografia
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bwmeta1.element.doi-10_2478_s11533-011-0028-9
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