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Volumn 7, Issue 6, 2003, Pages 1003-1042

The quantisation of poisson structures arising in chern-simons theory with gauge group G ⋉g

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EID: 11944255902     PISSN: 10950761     EISSN: 10950753     Source Type: Journal    
DOI: 10.4310/atmp.2003.v7.n6.a3     Document Type: Article
Times cited : (61)

References (36)
  • 1
    • 33744722968 scopus 로고
    • 2+1 dimensional gravity as an exactly soluble system
    • E. Witten, "2+1 dimensional gravity as an exactly soluble system", Nucl. Phys. B 311 (1988) 46-78.
    • (1988) Nucl. Phys. B , vol.311 , pp. 46-78
    • Witten, E.1
  • 2
    • 0039902474 scopus 로고
    • Combinatorial quantization of the Hamiltonian Chern-Simons Theory
    • A. Y. Alekseev, H. Grosse, V. Schomerus, "Combinatorial quantization of the Hamiltonian Chern-Simons Theory", Commun. Math. Phys. 172 (1995) 317-358.
    • (1995) Commun. Math. Phys. , vol.172 , pp. 317-358
    • Alekseev, A.Y.1    Grosse, H.2    Schomerus, V.3
  • 3
    • 0030542947 scopus 로고
    • Combinatorial quantization of the Hamiltonian Chern-Simons Theory II
    • A. Y. Alekseev, H. Grosse, V. Schomerus, "Combinatorial quantization of the Hamiltonian Chern-Simons Theory II", Commun. Math. Phys. 174 (1995) 561-604.
    • (1995) Commun. Math. Phys. , vol.174 , pp. 561-604
    • Alekseev, A.Y.1    Grosse, H.2    Schomerus, V.3
  • 4
    • 0000480877 scopus 로고    scopus 로고
    • Representation theory of Chern-Simons observables
    • A. Y. Alekseev, V. Schomerus, "Representation theory of Chern-Simons observables", Duke Math. Journal 85 (1996) 447-510.
    • (1996) Duke Math Journal , vol.85 , pp. 447-510
    • Alekseev, A.Y.1    Schomerus, V.2
  • 5
    • 0003149243 scopus 로고
    • Poisson structures on moduli of flat connections on Riemann surfaces and r-matrices
    • V. V. Fock, A. A. Rosly, "Poisson structures on moduli of flat connections on Riemann surfaces and r-matrices", ITEP preprint 72-92 (1992);
    • (1992) ITEP preprint , pp. 72-92
    • Fock, V.V.1    Rosly, A.A.2
  • 7
    • 0001360773 scopus 로고
    • The symplectic nature of fundamental groups of surfaces
    • W. M. Goldman, "The symplectic nature of fundamental groups of surfaces", Advances in Mathematics 54 (1984) 200-225.
    • (1984) Advances in Mathematics , vol.54 , pp. 200-225
    • Goldman, W.M.1
  • 8
    • 0000979746 scopus 로고
    • Yang-Mills equations over Riemann surfaces
    • M. Atiyah, R. Bott, "Yang-Mills equations over Riemann surfaces", Phil. Trans. R. Soc. London A 308 (1982) 523.
    • (1982) Phil. Trans. R. Soc. London , vol.A 308 , pp. 523
    • Atiyah, M.1    Bott, R.2
  • 9
    • 33646038770 scopus 로고
    • Symplectic structure of the moduli space of flat connections on a Riemann surface
    • A. Y. Alekseev, A. Z. Malkin, "Symplectic structure of the moduli space of flat connections on a Riemann surface", Commun. Math. Phys. 169 (1995) 99-119.
    • (1995) Commun. Math. Phys. , vol.169 , pp. 99-119
    • Alekseev, A.Y.1    Malkin, A.Z.2
  • 10
    • 0037871983 scopus 로고    scopus 로고
    • Poisson structure and symmetry in the Chern-Simons formulation of (2+1)-dimensional gravity
    • C. Meusburger, B. J. Schroers, "Poisson structure and symmetry in the Chern-Simons formulation of (2+1)-dimensional gravity", Class. Quant. Grav. 20 (2003) 2193-2233.
    • (2003) Class. Quant. Grav. , vol.20 , pp. 2193-2233
    • Meusburger, C.1    Schroers, B.J.2
  • 12
  • 13
    • 33744749425 scopus 로고
    • Symplectic structures associated to Lie-Poisson groups
    • A. Y. Alekseev, A. Z. Malkin, "Symplectic structures associated to Lie-Poisson groups", Commun. Math. Phys. 162 (1994) 147-173.
    • (1994) Commun. Math. Phys. , vol.162 , pp. 147-173
    • Alekseev, A.Y.1    Malkin, A.Z.2
  • 18
    • 33745040449 scopus 로고
    • On the principles of elementary quantum mechanics
    • H. Groenewold, "On the principles of elementary quantum mechanics", Physica 12 (1946) 405-460.
    • (1946) Physica , vol.12 , pp. 405-460
    • Groenewold, H.1
  • 19
    • 0002061573 scopus 로고
    • Sur certaines representations unitaires d'un groupe infini de transformations
    • L. van Hove, "Sur certaines representations unitaires d'un groupe infini de transformations", Memoirs de l'Academie Royale de Belgique (Classe des Sciences) 26(6) (1951) 61-102.
    • (1951) Memoirs de l'Academie Royale de Belgique (Classe des Sciences) , vol.26 , Issue.6 , pp. 61-102
    • Van Hove, L.1
  • 20
    • 0000775731 scopus 로고
    • Sur le problème des relations entre les transformations unitaires de la mécanique quantique et les transformations canoniques de la mecanique classique
    • L. van Hove, "Sur le problème des relations entre les transformations unitaires de la mécanique quantique et les transformations canoniques de la mecanique classique", Academie Royale de Belgique Bulletin de la Classe des Sciences 37(5) (1951) 610-620.
    • (1951) Academie Royale de Belgique Bulletin de la Classe des Sciences , vol.37 , Issue.5 , pp. 610-620
    • Van Hove, L.1
  • 21
    • 0004292992 scopus 로고
    • North Holland Publishing Company, Amsterdam
    • J. Dixmier, "Enveloping algebras", North Holland Publishing Company, Amsterdam, 1977.
    • (1977) Enveloping algebras
    • Dixmier, J.1
  • 25
    • 0040701973 scopus 로고
    • Operators and representation theory
    • Elsevier Science, Amsterdam
    • P. E. T. Jorgensen, "Operators and representation theory", North Holland Mathematical Studies 147, Elsevier Science, Amsterdam, 1988.
    • (1988) North Holland Mathematical Studies , vol.147
    • Jorgensen, P.E.T.1
  • 27
    • 51249195667 scopus 로고
    • Algèbres quasi-unitaires
    • J. Dixmier, "Algèbres quasi-unitaires", Comment. Math. Helvetici 26 (1952) 275-322.
    • (1952) Comment. Math. Helvetici , vol.26 , pp. 275-322
    • Dixmier, J.1
  • 28
    • 84972545069 scopus 로고
    • Families of induced representations
    • J. Glimm, "Families of induced representations", Pacific J. Math. 12 (1962) 885-911.
    • (1962) Pacific J. Math. , vol.12 , pp. 885-911
    • Glimm, J.1
  • 29
    • 21744455350 scopus 로고    scopus 로고
    • The quantum double of a (locally) compact group
    • T. Koornwinder, N. Muller, "The quantum double of a (locally) compact group", Journal of Lie Theory 7 (1997) 101-120.
    • (1997) Journal of Lie Theory , vol.7 , pp. 101-120
    • Koornwinder, T.1    Muller, N.2
  • 30
    • 0033474221 scopus 로고    scopus 로고
    • Harmonic analysis on the quantum Lorentz group
    • E. Buffenoir, P. Roche, "Harmonic analysis on the quantum Lorentz group", Commun. Math. Phys. 207 (1999) 499-555.
    • (1999) Commun. Math. Phys. , vol.207 , pp. 499-555
    • Buffenoir, E.1    Roche, P.2
  • 31
    • 0041428064 scopus 로고    scopus 로고
    • Hamiltonian Quantization of Chern-Simons theory with SL(2,C) Group
    • E. Buffenoir, K. Noui, P. Roche, "Hamiltonian Quantization of Chern-Simons theory with SL(2,C) Group", Class. Quant. Grav. 19 (2002) 4953-5016.
    • (2002) Class. Quant. Grav. , vol.19 , pp. 4953-5016
    • Buffenoir, E.1    Noui, K.2    Roche, P.3
  • 32
    • 0010596764 scopus 로고    scopus 로고
    • Combinatorial quantisation of Euclidean gravity in three dimensions
    • N. P. Landsman, M. Pflaum, M. Schlichenmaier (Eds.), Birkhäuser, in: Progress in Mathematics
    • B. J. Schroers, "Combinatorial quantisation of Euclidean gravity in three dimensions", in: N. P. Landsman, M. Pflaum, M. Schlichenmaier (Eds.), "Quantization of singular symplectic quotients", Birkhäuser, in: Progress in Mathematics, Vol. 198, 2001, 307-328.
    • (2001) Quantization of singular symplectic quotients , vol.198 , pp. 307-328
    • Schroers, B.J.1
  • 33
    • 0003219350 scopus 로고
    • Elements of the theory of representations
    • Springer Verlag, Berlin
    • A. A. Kirillov, "Elements of the theory of representations", Grundlehren der mathematischen Wissenschaft 220, Springer Verlag, Berlin, 1976.
    • (1976) Grundlehren der mathematischen Wissenschaft , vol.220
    • Kirillov, A.A.1
  • 35
    • 0032210406 scopus 로고    scopus 로고
    • Tensor product representatiosn of the quantum double of a compact group
    • T. Koornwinder, N. Muller, F. A. Bais, "Tensor product representatiosn of the quantum double of a compact group", Commun. Math. Phys 198 (1998) 157-186.
    • (1998) Commun. Math. Phys. , vol.198 , pp. 157-186
    • Koornwinder, T.1    Muller, N.2    Bais, F.A.3
  • 36
    • 0032511696 scopus 로고    scopus 로고
    • Topological field theory and the quantum double of SU(2)
    • F. A. Bais, N. Muller, "Topological field theory and the quantum double of SU(2)", Nucl. Phys. B530 (1998) 349-400.
    • (1998) Nucl. Phys. , vol.B530 , pp. 349-400
    • Bais, F.A.1    Muller, N.2


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