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Imprimitivity theorem for groupoid representations

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Wybrane pełne teksty z tego czasopisma
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Języki publikacji
EN
Abstrakty
EN
We define and investigate the concept of the groupoid representation in- duced by a representation of the isotropy subgroupoid. Groupoids in question are locally compact transitive topological groupoids. We formulate and prove the imprimitivity theorem for such representations which is a generalization of the classical Mackey's theorem known from the theory of group representations.
Wydawca
Rocznik
Strony
29--48
Opis fizyczny
Bibliogr. 24 poz.
Twórcy
autor
  • Department of Mathematics and Information Science Warsaw University of Technology Plac Politechniki 1 00-661 Warsaw, Poland
Bibliografia
  • [1] R. Bos, Continuous representations of groupoids, arXiv:math/0612639v3 [math.RT].
  • [2] R. Brown, From groups to groupoids, Bull. London Math. Soc. 19 (1987), 113–134.
  • [3] M. R. Buneci, Groupoid C*-algebras, Surveys in Mathematics and its Applications, ISSN 1842-6298, 1 (2006), 71-98.
  • [4] A. Cannas da Silva, A. Weinstein, Geometric Models for Noncommutative Algebras, American Mathematical Society, Berkeley, (1999).
  • [5] J. Dixmier, Von Neumann Algebras, North Holland Publ. Comp., Amsterdam, (1981).
  • [6] M. Heller, Z. Odrzygóźdź, L. Pysiak, W. Sasin, Structure of malicious singularities, Int. J. Theor. Phys. 42 (2003), 427–441.
  • [7] M. Heller, L. Pysiak, W. Sasin, Noncommutative unification of general relativity and quantum mechanics, J. Math. Phys. 46 (2005), 122501–15.
  • [8] M. Heller, L. Pysiak, W. Sasin, Noncommutative dynamics of random operators, Int. J. Theor. Phys. 44 (2005), 619–628.
  • [9] M. Heller, L. Pysiak, W. Sasin, Conceptual unification of gravity and quanta, Int. J.Theor. Phys. 46 (2007), 2494–2512.
  • [10] M. Heller, Z. Odrzygóźdź, L. Pysiak, W. Sasin, Gravitational Aharonov–Bohm effect, Int. J. Theor. Phys. 47 (2008), 2566–2575.
  • [11] N. P. Landsman, Mathematical Topics between Classical and Quantum Mechanics, Springer, New York, (1998).
  • [12] K. C. H. Mackenzie, Lie Groupoids and Lie Algebroids in Differential Geometry, London Math. Society Lecture Notes Series, 124, Cambridge University Press, Cambridge, (1987).
  • [13] G. W. Mackey, The relationship between classical mechanics and quantum mechanics, Contemporary Math. 214 (1998), 91–109.
  • [14] G. W. Mackey, Unitary group representations in physics, probability and number theory, Benjamin, Reading, Mass. (1978).
  • [15] G. W. Mackey, Induced representations of locally compact groups I,II, Acta Math. 55 (1952), 101–139; 58 (1953), 193–221.
  • [16] G. W. Mackey, Imprimitivity for representations of locally compact groups, Proc. Nat. Acad. Sci. U.S.A. 35 (1949), 537–545.
  • [17] J. A. Packer, Applications of the work of Stone and von Neumann to the theory of wavelets, Contemporary Math. 365 (2004), 253–279.
  • [18] A. L. T. Paterson, Groupoids, Inverse Semigroups, and their Operators Algebras, Birkhauser, Boston (1999).
  • [19] L. Pysiak, Time flow in a noncommutative regime, Internat. J. Theoret. Phys. 46 (1) (2007), 16–30.
  • [20] L. Pysiak, Groupoids, their representations and imprimitivity systems, Demonstratio Math. 37 (2004), 661–670.
  • [21] J. N. Renault, A groupoid approach to C*-algebras, Lecture Notes in Math. 793, Springer-Verlag, New York (1980).
  • [22] M. E. Taylor, Noncommutative Harmonic Analysis, A. M. S., Providence (1986).
  • [23] A. Weinstein, Groupoids: unifying internal and external geometry, Contemp. Math. 282 (2001), 1–19.
  • [24] J. Westman, Harmonic analysis on groupoids, Pacific J. Math. 27 (1968), 621–632.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA4-0031-0021
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