易量子群与半直积量子群的量子子群
Easy quantum groups and quantum subgroups of a semi-direct product quantum group
摘要：
考虑紧致矩阵量子群，其基本余表示矩阵的元素是具有中心支撑的部分等距。我们证明了这样的量子群有一个简单的表示，即一个群对偶量子群在一个置换群的作用下的半直积量子群。这个一般性结果使我们能够通过某些反射群对具有上述性质的易量子群进行完全分类。我们给出了四个应用我们的结果。首先，有无数的易量子群。第二，在自由正交量子群和置换群之间存在非易量子群。第三，研究了超八面体级数的算子代数性质。最后，我们证明了一个广义的de Finetti定理，容易量子群在这篇文章的范围。
英文摘要：
We consider compact matrix quantum groups whose fundamental corepresentation matrix has entries which are partial isometries with central support. We show that such quantum groups have a simple representation as semi-direct product quantum groups of a group dual quantum group by an action of a permutation group. This general result allows us to completely classify easy quantum groups with the above property by certain reflection groups. We give four applications of our result. First, there are uncountably many easy quantum groups. Second, there are non-easy quantum groups between the free orthogonal quantum group and the permutation group. Third, we study operator algebraic properties of the hyperoctahedral series. Finally, we prove a generalised de Finetti theorem for easy quantum groups in the scope of this article.
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