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http://yadda.icm.edu.pl:80/baztech/element/bwmeta1.element.baztech-article-PWA5-0018-0024

Czasopismo

Demonstratio Mathematica

Tytuł artykułu

Inner geometry of random operators

Autorzy Heller, M.  Pysiak, L.  Sasin, W. 
Treść / Zawartość https://www.degruyter.com/view/j/dema
Warianty tytułu
Języki publikacji EN
Abstrakty
EN If V is a foliated manifold, there exists a von Neumann algebra M associated with V. We consider the case when V is a transformation groupoid gamma and the von Neumann algebra M associated with gamma is a noncommutative algebra of random operators. We show that M is generated by a functional algebra A defined on the groupoid gamma with a noncommutative convolution as multiplication, and develop the differential geometry (metric, connection and curvature) based on inner derivations of the algebra A.
Słowa kluczowe
PL operatory losowe   geometria nieprzemienna   geometria wewnętrzna   grupoidy  
EN random operators   noncommutative geometry   inner geometry   groupoids  
Wydawca De Gruyter
Czasopismo Demonstratio Mathematica
Rocznik 2006
Tom Vol. 39, nr 4
Strony 971--978
Opis fizyczny Bibliogr. 9 poz.
Twórcy
autor Heller, M.
autor Pysiak, L.
autor Sasin, W.
Bibliografia
[1] O. Bratteli and D. W. Robinson, Operator Algebras and Quantum Statistical Mechanics, vol. 1, Springer, New York, 1979.
[2] A. Connes, Noncommutative Geometry, Academic Press, New York-London, 1994.
[3] M. Heller, Z. Odrzygóźdź, L. Pysiak and W. Sasin, Noncommutative unification of general relativity and quantum mechanics. A finite model, Gen. Relativity and Gravitation 36 (2004), 111–126.
[4] M. Heller, L. Pysiak andW. Sasin, Noncommutative unification of general relativity and quantum mechanics, J. Math. Phys. 46 (2005), 122501-16.
[5] M. Heller, L. Pysiak andW. Sasin, Noncommutative dynamics of random operators, Int. J. Theor. Phys. 44 (2005), 619–628.
[6] L. T. Paterson, Groupoids, Inverse Semigroups, and Their Operator Algebras, Birkhauser, Boston–Basel–Berlin, 1998.
[7] L. Pysiak, Time flow in a noncommutative regime, Int. J. Theor. Phys., in press.
[8] L. Pysiak, M. Heller, Z. Odrzygóźdź and W. Sasin, Observables in a noncommutative approach to the unification of quanta and gravity: a finite model, Gen. Relativity Gravitation 37 (2005), 541–555.
[9] L. Pysiak, M. Heller and W. Sasin, Axiomatic formulation of the groupoid approach to the unification of relativity and quanta, to be published.
Kolekcja BazTech
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