论文标题
二多数代数中微积分的函子
Functors of Differential Calculus in Diolic Algebras
论文作者
论文摘要
我们为研究矢量束的差分演算提供了一种新的代数形式主义。这是通过研究任意分级的交换代数（DCGCA）的差分演算的各种函子，并将该语言应用于这项工作中引入的特别简单的两组分级对象，我们称之为二多数代数。这种微积分的概念方法的一个显着特征是，它从普通的差异，符号和泊松几何形状中恢复了许多知名的对象和概念，但也提供了一些独特的方面，这些方面具有其自身的独立兴趣。
We pose a new algebraic formalism for studying differential calculus in vector bundles. This is achieved by studying various functors of differential calculus over arbitrary graded commutative algebras (DCGCA) and applying this language to a particularly simple class of two-component graded objects introduced in this work, that we call Diolic algebras. A salient feature of this conceptual approach to calculus is that it recovers many well-known objects and notions from ordinary differential, symplectic and Poisson geometry but also provides some unique aspects, which are of their own independent interest.
