×

Flat connections and polyubles. (English. Russian original) Zbl 0849.58030

Theor. Math. Phys. 95, No. 2, 526-534 (1993); translation from Teor. Mat. Fiz. 95, No. 2, 228-238 (1993).
Summary: 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.

MSC:

37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
58D27 Moduli problems for differential geometric structures
53C07 Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Axelrod S., Witten E., Della Pietra S. Geometric quantization of Chern-Simons gauge theory. Preprint IASSNS-HEP-89/57. · Zbl 0697.53061
[2] Witten E. On Quantum Gauge Theory in Two Dimensions. Preprint IASSNS-HEP-91/3. · Zbl 0762.53063
[3] A. Bilal, Fock V.V., Kogan I.I. On the origin ofW-algebras.// Nucl. Phys. 1991. V. B359. 2-3, P. 635-672. · doi:10.1016/0550-3213(91)90075-9
[4] Narasimhan M.S., Ramanan S. Deformations of moduli space of vector bundles over an Algebraic Curve.// Ann. Math. 1975. V. 101. P. 31-34. · Zbl 0314.14004 · doi:10.2307/1970933
[5] Atiyah M., Bott R. The Yang-Mills Equations over a Riemann Surface.// Phil. Trans. Roy. Soc. Lond. 1982. V. A308. P. 523. · Zbl 0509.14014
[6] Beilinson A.A., Drinfeld V.G., Ginzburg V.A. Differential Operators on Moduli Space ofG-bundles: Preprint.
[7] Hitchin N. Stable Bundles and Integrable Systems.// Duke. Math. J. 1987. V. 54. P. 97-114. · Zbl 0627.14024 · doi:10.1215/S0012-7094-87-05408-1
[8] Semenov-Tian-Shansky M.A. Dressing Transformations and Poisson Group Actions. Publ. RIMS Kyoto Univ. 1985. V. 21. P. 1237-1260. · Zbl 0674.58038 · doi:10.2977/prims/1195178514
[9] 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.
[10] Alekseev A., Faddeev L., Semenov-Tian-Shansky M. Hidden Quantum Group inside Kac-Moody Algebra. Preprint LOMI E-5-91. · Zbl 0798.17008
[11] 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.
[12] Weinstein A. The Local Structure of Poisson Manifolds.// J. Diff. Geom. 1983. V. 18. P. 523-557. · Zbl 0524.58011
[13] Fock V.V., Rosly A.A. Poisson structure on moduli of flat connections on Riemann surfaces andr-matrix. Preprint ITEP-72-92. · Zbl 0945.53050
[14] Faddeev L.D., Takhtadjan L.A. Hamiltonian Approach in Soliton Theory, M.: Nauka, 1986.
[15] 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.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.