Atiyah classes of three-dimensional real Lie bialgebras

Let (g,g*,γ) be a Lie bialgebra,where the map γ: g→gg is a 1-cocycle,that is, [γ]∈H(g,gg). First, the definition of Atiyah class of a Lie bialgebra based on the map γ was given. Combining the classification results of three-dimensional real Lie bialgebras, Atiyah classes of these Lie bialgebras were computed and analyzed.