论文标题
在$（σ，τ）$ - 代数的几何形状上
On the geometry of $(σ,τ)$-algebras
论文作者
论文摘要
我们介绍$（σ，τ）$ - 代数作为非交通型微积分的框架，以及换向的代数，具有$σ$衍生和量子群的动机。 $（σ，τ）$ - 代数由一个关联代数和一组$（σ，τ）$ - 派生组成，并引入了$（σ，τ）$ - 模块和连接的相应概念。我们证明，$（σ，τ）$ - 连接在投影模块上存在，并引入了扭转和曲率的概念，以及与Hermitian形式的兼容性，从而定义了Levi-Civita $（σ，τ）$ - 连接的定义。为了说明新颖的概念，我们考虑$（σ，τ）$ - 代数和矩阵代数上的连接。
We introduce $(σ,τ)$-algebras as a framework for twisted differential calculi over noncommutative, as well as commutative, algebras with motivations from the theory of $σ$-derivations and quantum groups. A $(σ,τ)$-algebra consists of an associative algebra together with a set of $(σ,τ)$-derivations, and corresponding notions of $(σ,τ)$-modules and connections are introduced. We prove that $(σ,τ)$-connections exist on projective modules, and introduce notions of both torsion and curvature, as well as compatibility with a hermitian form, leading to the definition of a Levi-Civita $(σ,τ)$-connection. To illustrate the novel concepts, we consider $(σ,τ)$-algebras and connections over matrix algebras in detail.
