Quantum groupoids of the finite type and quantization on orbit spaces

• Autorzy: Heller M. , Odrzygóźdź Z. , Pysiak L. , Sasin W.
• Języki publikacji: EN

Abstrakty

EN

We show that the Hopf algebra on a transformation groupoid F = E x G where G is a finite group acting on the total space of a principal fibre boundle over M = E/G, is the cross product of the algebras C°°(E) and CG. We study duality properties of this algebra, and consider quantization on orbit spaces program in this context.

Słowa kluczowe

EN

groupoids; orbit space; quantization

PL

grupoidy; przestrzeń orbitalna; kth lower record

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2004
• Tom: Vol. 37, nr 3
• Strony: 671--678
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Heller M.

• Vatican Observatory, V-00120 Vatican City State [correspondence adress: ul. Powstańców Warszawy 13/94, 33-110 Tarnów, Poland]

autor

Odrzygóźdź Z.

• Faculty of Mathematics and Information Science, Warsaw University of Technology, Plac Politechniki 1, 00-661 Warsaw, Poland

autor

Pysiak L.

• Faculty of Mathematics and Information Science, Warsaw University of Technology, Plac Politechniki 1, 00-661 Warsaw, Poland

autor

Sasin W.

• Faculty of Mathematics and Information Science, Warsaw University of Technology, Plac Politechniki 1, 00-661 Warsaw, Poland

Bibliografia

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• [4] N. P. Landsman, Induced representations, Gauge Fields, and quantization on homogeneous spaces, Rev. Math. Phys. 4 (1992), 503-527.
• [5] N. P. Landsman, The Quantization of Constrained Systems: From Symplectic Reduction to Rieffel Induction, dg-ga/9601009 vl, 1996.
• [6] G. M. Mackey, The Theory of Unitary Group Representations, University of Chicago Press, Chicago, 1976.
• [7] S. Majid, Foundations of Quantum Group Theory, Cambridge University Press, Cambridge, 2000.
• [8] S. Majid, Quantum groups and noncommutative geometry, J. Math. Phys. 41 (2000), 3892-3942.
• [9] G. Maltsiniotis, Groupoids quantiques, C. R. A. S. 314 (1992), 249-252.
• [10] G. Maltsiniotis, Groupoids quantiques de base non commutative, Comm. Algebra 28 (2000), 3441-3501.
• [11] D. Nikshych, and L. Vainerman, Algebraic Versions of a Finite-Dimensional Quantum Groupoid, Lecture Notes in Pure and Appl. Math. 209 (2000), 189-221.
• [12] D. Nikshych, and L. Vainerman, Finite Quantum Groupoids and Their Applications, math.QA/0006057 v2, 2000.