论文标题
差异群体和范定理的差异共同点
Cohomologies of difference Lie groups and van Est theorem
论文作者
论文摘要
差异组是一个配备差异操作员的谎言组，相对于伴随作用等效地等同于交叉的同态。在本文中，首先，我们介绍了差异群体的表示的概念，并通过分化和整合来建立差异群体的表示与差异代数的表示之间的关系。然后，我们介绍了一个差异群体的共同论理论，并通过范式定理为其辩护。最后，我们使用第二个共同体学组将差异组的Abelian扩展分类为应用。
A difference Lie group is a Lie group equipped with a difference operator, equivalently a crossed homomorphism with respect to the adjoint action. In this paper, first we introduce the notion of a representation of a difference Lie group, and establish the relation between representations of difference Lie groups and representations of difference Lie algebras via differentiation and integration. Then we introduce a cohomology theory for difference Lie groups and justify it via the van Est theorem. Finally, we classify abelian extensions of difference Lie groups using the second cohomology group as applications.
