论文标题
HOPF代数，双模型连接和非交换性几何形状
Hopf Algebroids, Bimodule Connections and Noncommutative Geometry
论文作者
论文摘要
我们构建了由非交通性几何形状引起的左双方和HOPF代数的新示例。给定代数$ a $上的一阶差分微积分$ω$，左图$ \ mathfrak {x} $的空间，我们构造了左$ A $ a $ a $ -bialgeroid $ b \ mathfrak {x} $，其左模量的类别对左BIMODULE连接的类别是等值的。当$ω$是一个关键的bimodule时，我们通过限制在与$ω$和$ \ mathfrak {x} $相互结合的BiModule连接子类别中构建了$ a $上的Hopf代数$ H \ Mathfrak {X} $。假设2形式的$ω^{2} $也是关键的，我们为平坦的bimodule Connections构造了相应的Hopf algebroid $ \ Mathcal {d} \ Mathfrak {x} $，并恢复lie-rine-rinehart hopf algebroids的构造，以恢复lie-rine-rinehart hopf algebroids。我们使用这些构造来提供非共同基础上Hopf代数的明确示例。
We construct new examples of left bialgebroids and Hopf algebroids, arising from noncommutative geometry. Given a first order differential calculus $Ω$ on an algebra $A$, with the space of left vector fields $\mathfrak{X}$, we construct a left $A$-bialgeroid $B\mathfrak{X}$, whose category of left modules is isomorphic to the category of left bimodule connections over the calculus. When $Ω$ is a pivotal bimodule, we construct a Hopf algebroid $H\mathfrak{X}$ over $A$, by restricting to a subcategory of bimodule connections which intertwine with both $Ω$ and $\mathfrak{X}$ in a compatible manner. Assuming the space of 2-forms $Ω^{2}$ is pivotal as well, we construct the corresponding Hopf algebroid $\mathcal{D}\mathfrak{X}$ for flat bimodule connections, and recover Lie-Rinehart Hopf algebroids as a quotient of our construction in the commutative case. We use these constructions to provide explicit examples of Hopf algebroids over noncommutative bases.
