实数域上三维李双代数的Atiyah class

Atiyah classes of three-dimensional real Lie bialgebras

摘要: 设(g,g*,γ)是一个李双代数,这里γ∶g→gg是1闭上链,即γ∈H(g,gg).首先通过γ给出了李双代数(g,g*,γ)的Atiyah class 的定义,然后结合实数域上所有三维李双代数的分类情况,计算并讨论了这些李双代数的Atiyah class.

Abstract: 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.