论文标题
有限的量子超组
Finite quantum hypergroups
论文作者
论文摘要
有限的量子超组是一个有限的Unitial Algebra $ a $在复数上。 $ a $上有一个共同点，这是一张共同点的地图，从$ a $到$ a \ otimes a $假定是Unital的，但不需要是代数同构。有一个应该是同态的国家。最后，主要的额外要求是存在与正确属性的忠实左派积分。对于这样有限的量子超组，可以构造双重。它再次是有限的量子超级组。在\ cite {de-vd1，de-vd2}中研究了代数量子超组的更一般概念。如果代数量子超级组的基本代数是有限维数，则在本文的意义上，它是有限的量子超组。在这里，我们独立对待有限的量子超级组，重点是该概念的发展。它旨在阐明\ cite {la-vd3a}和\ cite {la-vd3b}中采取的各种步骤。在\ cite {la-vd3b}中，我们介绍并研究了量子超组的更一般概念。它不仅包含来自\ cite {de-vd1}的代数量子高组，还包含一些拓扑案例。我们自然会遇到这些量子超级组，在我们的双核生产工作中，请参见\ cite {la-vd4，la-vd5，la-vd7}。我们包括一些例子来说明理论。一种来自有限的组和一个子组。其他示例取自双杂种理论。
A finite quantum hypergroup is a finite-dimensional unital algebra $A$ over the field of complex numbers. There is a coproduct on $A$, a coassociative map from $A$ to $A\otimes A$ assumed to be unital, but it is not required to be an algebra homomorphism. There is a counit that is supposed to be a homomorphism. Finally, the main extra requirement is the existence of a faithful left integral with the right properties. For such a finite quantum hypergroup, the dual can be constructed. It is again a finite quantum hypergroup. The more general concept of an algebraic quantum hypergroup is studied in \cite{De-VD1, De-VD2}. If the underlying algebra of an algebraic quantum hypergroup is finite-dimensional, it is a finite quantum hypergroup in the sense of this paper. Here we treat finite quantum hypergroups independently with an emphasis on the development of the notion. It is meant to clarify the various steps taken in \cite{La-VD3a} and \cite{La-VD3b}. In \cite{La-VD3b} we introduce and study a still more general concept of quantum hypergroups. It not only contains the algebraic quantum hypergroups from \cite{De-VD1}, but also some topological cases. We naturally encounter these quantum hypergroups in our work on bicrossproducts, see \cite{La-VD4, La-VD5, La-VD7}. We include some examples to illustrate the theory. One kind is coming from a finite group and a subgroup. The other examples are taken from the bicrossproduct theory.
