Observables in $2+1$ Gravity and Noncommutative Teichmüller Spaces
Teoretičeskaâ i matematičeskaâ fizika, Tome 129 (2001) no. 2, pp. 360-368 Cet article a éte moissonné depuis la source Math-Net.Ru

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The algebra of quantum geodesics obtained by quantizing the coordinates of the Teichmüller spaces is the Nelson–Regge quantum $so_q(m)$ algebra of monodromies (Wilson loops) in the Chern–Simons theory, which provides an effective description of $(2+1)$-dimensional gravity.
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     title = {Observables in $2+1$ {Gravity} and {Noncommutative} {Teichm\"uller} {Spaces}},
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L. O. Chekhov. Observables in $2+1$ Gravity and Noncommutative Teichmüller Spaces. Teoretičeskaâ i matematičeskaâ fizika, Tome 129 (2001) no. 2, pp. 360-368. http://geodesic.mathdoc.fr/item/TMF_2001_129_2_a14/

[1] E. Verlinde and H. Verlinde, “Conformal field theory and geometric quantization”, Superstrings (1989), World Scientific, River Edge, NJ, 1990, 422 | MR | Zbl

[2] V. V. Fok, L. O. Chekhov, TMF, 120:3 (1999), 511 | DOI | MR

[3] V. V. Fok, L. O. Chekhov, Tr. MIAN, 226, 1999, 163 | MR

[4] J. E. Nelson and T. Regge, Nucl. Phys. B, 328 (1989), 190 ; J. E. Nelson, T. Regge, and F. Zertuche, Nucl. Phys. B, 339 (1990), 516 | DOI | MR | DOI | MR

[5] J. E. Nelson and T. Regge, Phys. Lett. B, 272 (1991), 213 ; Commun. Math. Phys., 155 (1993), 561 | DOI | MR | DOI | MR | Zbl

[6] V. V. Fock, Combinatorial description of the moduli space of projective structures, E-print hep-th/9312193

[7] W. M. Goldman, Invent. Math., 85 (1986), 263 | DOI | MR | Zbl

[8] L. D. Faddeev, Lett. Math. Phys., 34 (1995), 249 | DOI | MR | Zbl

[9] R. M. Kashaev, Quantization of Teichmüller spaces and the quantum dilogarithm, E-print q-alg/9705021 | MR

[10] V. G. Turaev, Ann. Scient. \hboxÉc. Norm. Sup. Ser. 4, 24 (1991), 635 | MR | Zbl

[11] M. Havlíček, A. V. Klimyk, and S. Pošta, Representations of the cyclically symmetric $q$-deformed algebra $so_q(3)$, E-print math.qa/9805048 | MR

[12] M. Ugaglia, On a Poisson structure on the space of Stokes matrices, E-print math.ag/9902045 | MR

[13] A. Bondal, A symplectic groupoid of triangular bilinear forms and the braid groups, Preprint IHES/M/00/02 | MR