论文标题
具有任何权重的差分代数的共同体，扩展和变形
Cohomologies, extensions and deformations of differential algebras with any weights
论文作者
论文摘要
作为对微分方程的代数研究，已经研究了一个世纪的差分代数，并成为数学的重要领域。近年来，该领域已将其用于非共同的关联和谎言代数环境，并在操作员身份具有权重以包括差异操作员和差异代数的情况下。本文为任何权重的差异代数提供了一个共同体学理论。这为零重量案例提供了一种统一的方法，这与早期对差分代数的研究相似，而非零重量案例则带来了新的挑战。作为应用，差异代数的阿贝尔扩展由第二个同胞组分类。此外，还获得了差异代数的形式变形，并且差异代数的刚性以消失的第二个共同体学组的消失为特征。
As an algebraic study of differential equations, differential algebras have been studied for a century and and become an important area of mathematics. In recent years the area has been expended to the noncommutative associative and Lie algebra contexts and to the case when the operator identity has a weight in order to include difference operators and difference algebras. This paper provides a cohomology theory for differential algebras of any weights. This gives a uniform approach to both the zero weight case which is similar to the earlier study of differential Lie algebras, and the non-zero weight case which poses new challenges. As applications, abelian extensions of a differential algebra are classified by the second cohomology group. Furthermore, formal deformations of differential algebras are obtained and the rigidity of a differential algebra is characterized by the vanishing of the second cohomology group.
