On Deformation Quantization of Poisson–Lie Groups and Moduli Spaces of Flat Connections: Fig. 1.

2014 ◽  
Vol 2015 (15) ◽  
pp. 6734-6751 ◽  
Author(s):  
David Li-Bland ◽  
Pavol Ševera
Keyword(s):  
Lie Groups ◽  
Moduli Spaces ◽  
Deformation Quantization ◽  
Flat Connections ◽  
Poisson Lie Groups

scholarly journals Poisson–Lie Groups and Gauge Theory

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1324
Author(s):  
Catherine Meusburger
Keyword(s):  
Gauge Theory ◽  
Lie Groups ◽  
Moduli Spaces ◽  
Integrable Systems ◽  
Mathematical Physics ◽  
Flat Connections ◽  
Poisson Lie Groups ◽  
Chern Simons

We review Poisson–Lie groups and their applications in gauge theory and integrable systems from a mathematical physics perspective. We also comment on recent results and developments and their applications. In particular, we discuss the role of quasitriangular Poisson–Lie groups and dynamical r-matrices in the description of moduli spaces of flat connections and the Chern–Simons gauge theory.

Moduli Space of Flat Connections as a Poisson Manifold

1997 ◽  
Vol 11 (26n27) ◽  
pp. 3195-3206 ◽  
Author(s):  
V. V. Fock ◽  
A. A. Rosly
Keyword(s):  
Riemann Surface ◽  
Lie Groups ◽  
Poisson Structure ◽  
Moduli Space ◽  
Poisson Manifold ◽  
Gauge Fields ◽  
Two Dimensional ◽  
Flat Connections ◽  
Lattice Gauge ◽  
Poisson Lie Groups

In this talk we describe the Poisson structure of the moduli space of flat connections on a two dimensional Riemann surface in terms of lattice gauge fields and Poisson–Lie groups.

scholarly journals On the Connectedness of Moduli Spaces of Flat Connections over Compact Surfaces

2004 ◽  
Vol 56 (6) ◽  
pp. 1228-1236 ◽  
Author(s):  
Nan-Kuo Ho ◽  
Chiu-Chu Melissa Liu
Keyword(s):  
Lie Groups ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Orientable Surface ◽  
Equivalence Classes ◽  
Nonorientable Surface ◽  
Flat Connections ◽  
Gauge Equivalence ◽  
Compact Orientable Surface ◽  
Simply Connected

AbstractWe study the connectedness of the moduli space of gauge equivalence classes of flat G-connections on a compact orientable surface or a compact nonorientable surface for a class of compact connected Lie groups. This class includes all the compact, connected, simply connected Lie groups, and some non-semisimple classical groups.

POISSON–LIE GROUPS AND CLASSICAL W-ALGEBRAS

1992 ◽  
Vol 07 (05) ◽  
pp. 853-876 ◽  
Author(s):  
V. A. FATEEV ◽  
S. L. LUKYANOV
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Quantum Group ◽  
Lie Groups ◽  
Group Structure ◽  
Two Dimensional ◽  
Poisson Structures ◽  
Additional Symmetries ◽  
Conformal Field ◽  
Poisson Lie Groups

This is the first part of a paper studying the quantum group structure of two-dimensional conformal field theory with additional symmetries. We discuss the properties of the Poisson structures possessing classical W-invariance. The Darboux variables for these Poisson structures are constructed.

scholarly journals Dual Lie algebras of Heisenberg Poisson Lie groups

1993 ◽  
Vol 17 (2) ◽  
pp. 429-441
Author(s):  
Kentaro Mikami ◽  
Fumio Narita
Keyword(s):  
Lie Groups ◽  
Lie Algebras ◽  
Poisson Lie Groups
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