论文标题
HOPF代数的指数地图
The Exponential Map for Hopf Algebras
论文作者
论文摘要
我们在Hopf $*$ - 具有差分微积分的代数的Lie组上给出了经典的指数图。与经典案例的主要区别在于对指数图的价值的解释，这是谎言组的元素。我们将解释作为Hopf代数的状态，$ \ frac {1} {1} {2} $ bimodule的Hilbert $ c^{*} {2} $ bimodule的元素。我们在组上为复杂有价值的功能提供了示例$ s_ {3} $和$ \ mathbb {z} $，woronowicz的矩阵量子组$ \ mathbb {c} _ {q} _ {q} [su_2] $和Sweedler-Taft Algebra。
We give an analogue of the classical exponential map on Lie groups for Hopf $*$-algebras with differential calculus. The major difference with the classical case is the interpretation of the value of the exponential map, classically an element of the Lie group. We give interpretations as states on the Hopf algebra, elements of a Hilbert $C^{*} $-bimodule of $\frac{1}{2}$ densities and elements of the dual Hopf algebra. We give examples for complex valued functions on the groups $S_{3}$ and $\mathbb{Z}$, Woronowicz's matrix quantum group $\mathbb{C}_{q}[SU_2] $ and the Sweedler-Taft algebra.
