论文标题
紧凑量量子组的连接性和高斯零件
Connectedness and Gaussian Parts for Compact Quantum Groups
论文作者
论文摘要
我们介绍了紧凑型量子组的高斯部分$ \ mathbb {g} $，即$ \ mathbb {g} $的最大量子子群，支持$ \ mathbb {g} $的所有高斯功能。我们证明，高斯部分始终包含在KAC部分中，并且表征了经典紧凑型组的高斯部分，经典离散组的双重和紧凑型Lie组的$ Q $ - 指标。事实证明，这一概念与“牢固连接性”的新概念有关，我们展示了几个既连接又完全断开紧凑型量子群的示例。
We introduce the Gaussian part of a compact quantum group $\mathbb{G}$, namely the largest quantum subgroup of $\mathbb{G}$ supporting all the Gaussian functionals of $\mathbb{G}$. We prove that the Gaussian part is always contained in the Kac part, and characterise Gaussian parts of classical compact groups, duals of classical discrete groups and $q$-deformations of compact Lie groups. The notion turns out to be related to a new concept of "strong connectedness" and we exhibit several examples of both strongly connected and totally strongly disconnected compact quantum groups.
