论文标题
量子自动形态组的交叉产品等效性
Crossed Product Equivalence of Quantum Automorphism Groups
论文作者
论文摘要
我们比较有限维c $^\ ast $ -Algebra $ b $的量子自动形态组的代数，其中包括量子置换组$ s_n^+$，其中$ n = \ n = \ dim b $。我们表明，有限的Abelian Group $γ$通过痕量保护动作的矩阵放大和越过产品导致同构$ \ ast $ -Algebras。这使我们能够传输各种属性，例如内部单位性，嵌入性和强大的$ 1 $结合度，与这些量子组相关的各个代数之间。
We compare the algebras of the quantum automorphism group of finite-dimensional C$^\ast$-algebra $B$, which includes the quantum permutation group $S_N^+$, where $N = \dim B$. We show that matrix amplification and crossed products by trace-preserving actions by a finite Abelian group $Γ$ lead to isomorphic $\ast$-algebras. This allows us to transfer various properties such as inner unitarity, Connes embeddability, and strong $1$-boundedness between the various algebras associated with these quantum groups.
