Poisson–Lie Groups and Gauge Theory

Abstract

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.

Keywords

• Poisson–Lie groups
• Lie bialgebras and <i>r</i>-matrices
• integrable models
• Poisson homogeneous spaces