Abstract
The Poisson structure of the moduli space of flat connections on a two dimensional Riemann surface is described in terms of lattice gauge fields and Poisson-Lie groups.
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References
Axelrod S., Witten E., Della Pietra S. Geometric quantization of Chern-Simons gauge theory. Preprint IASSNS-HEP-89/57.
Witten E. On Quantum Gauge Theory in Two Dimensions. Preprint IASSNS-HEP-91/3.
A. Bilal, Fock V.V., Kogan I.I. On the origin ofW-algebras.// Nucl. Phys. 1991. V. B359. 2–3, P. 635–672.
Narasimhan M.S., Ramanan S. Deformations of moduli space of vector bundles over an Algebraic Curve.// Ann. Math. 1975. V. 101. P. 31–34.
Atiyah M., Bott R. The Yang-Mills Equations over a Riemann Surface.// Phil. Trans. Roy. Soc. Lond. 1982. V. A308. P. 523.
Beilinson A.A., Drinfeld V.G., Ginzburg V.A. Differential Operators on Moduli Space ofG-bundles: Preprint.
Hitchin N. Stable Bundles and Integrable Systems.// Duke. Math. J. 1987. V. 54. P. 97–114.
Semenov-Tian-Shansky M.A. Dressing Transformations and Poisson Group Actions. Publ. RIMS Kyoto Univ. 1985. V. 21. P. 1237–1260.
Alekseev A., Faddeev L., Semenov-Tian-Shansky M., Volkov A. The Unraveling of the Quantum Group Structure in WZNW Theory. Preprint CERN-TH-5981/91.
Alekseev A., Faddeev L., Semenov-Tian-Shansky M. Hidden Quantum Group inside Kac-Moody Algebra. Preprint LOMI E-5-91.
Turaev V.G. Algebras of Loops on Surfaces, Algebras of Knots, and Quantization. In: Braid Group, Knot Theory and Statistical Mechanics. Singapore, 1989. P. 80–93.
Weinstein A. The Local Structure of Poisson Manifolds.// J. Diff. Geom. 1983. V. 18. P. 523–557.
Fock V.V., Rosly A.A. Poisson structure on moduli of flat connections on Riemann surfaces andr-matrix. Preprint ITEP-72-92.
Faddeev L.D., Takhtadjan L.A. Hamiltonian Approach in Soliton Theory, M.: Nauka, 1986.
Ovsienko V.Yu., Khesin B.A. Gelfand-Dikey Bracket Symplectic Leaves and the Homotopy Classes of Nonflattened Curves// Funkts. Anal. Prilozhen. 1991. V. 24, 1, P. 38–48.
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Published in Teoreticheskaya i Matematicheskaya Fizika, Vol. 95, No. 2, pp. 228–238, May, 1993.
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Fock, V.V., Rosly, A.A. Flat connections and polyubles. Theor Math Phys 95, 526–534 (1993). https://doi.org/10.1007/BF01017138
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DOI: https://doi.org/10.1007/BF01017138