论文标题
相对差异的变形，共同体和整合代数
Deformations, cohomologies and integrations of relative difference Lie algebras
论文作者
论文摘要
在本文中，首先使用较高派生的括号，我们给出相对差的控制代数，该代数为代数，当动作是伴随作用时，当权重1的跨性同态或差分代数为1。然后，使用Getzler的扭曲$ L_ \ infty $ -Algebra，我们定义了代数相对差异的共同体。特别是，我们定义了差异的常规差异，该代数通过将差异的无限变形分类为代数。我们还定义了差异代数的差异的共同体，并在任意表示中具有系数，并使用第二个共同体学组对Abelian差异分类分类为代数代数。最后，我们表明，任何相对差异都可以以功能性方式集成到相对差异组。
In this paper, first using the higher derived brackets, we give the controlling algebra of relative difference Lie algebras, which are also called crossed homomorphisms or differential Lie algebras of weight 1 when the action is the adjoint action. Then using Getzler's twisted $L_\infty$-algebra, we define the cohomology of relative difference Lie algebras. In particular, we define the regular cohomology of difference Lie algebras by which infinitesimal deformations of difference Lie algebras are classified. We also define the cohomology of difference Lie algebras with coefficients in arbitrary representations, and using the second cohomology group to classify abelian extensions of difference Lie algebras. Finally, we show that any relative difference Lie algebra can be integrated to a relative difference Lie group in a functorial way.
