Inner geometry of random operators

• Autorzy: Heller M. , Pysiak L. , Sasin W.
• 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

EN

random operators; noncommutative geometry; inner geometry; groupoids

PL

operatory losowe; geometria nieprzemienna; geometria wewnętrzna; grupoidy

• 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.

• Correspondence address: ul. Powstańców Warszawy 13/94 33-110 Tarnów, Poland,

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.