论文标题
关于C* - 代数的异常对称的评论
Remarks on anomalous symmetries of C*-algebras
论文作者
论文摘要
对于组$ g $和$ g $和$ω\ in z^{3}（g，\ text {u}（1））$，在c*-algebra $ b $上进行的$ω$ - 反对动作是$ \ text {u}（u}（1）$ - 线性单线函数 - 2 groups $ \ text text text {2-group text {2-gr} {2-gr}（2-gr} {2-gr}（2-gr}（2-gr}（u}）（2-gr}（2-gr}（U} u}（u} u}（2-gr）， ω）\ rightarrow \ underline {\ text {aut}}（b）$，其中后者表示$*$ - $ b $的2组自动形态。类$ [ω] \ in H^{3}（g，\ text {u}（1））$称为动作的异常。我们显示每$ n \ ge 2 $和每个有限的组$ g $，每个异常都可以在稳定稳定的C*-Algebra $ c（m）\ otimes \ otimes \ Mathcal {k} $中，对于某些封闭的连接$ n $ -Manifold $ m $。我们还表明，尽管没有反对粗处的Roe C*代数异常的对称性，但对于每个有限的组$ G $，但在Roe Corona $ c^{*}（x）/\ Mathcal {k} $ a $ x $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ c $ a $ a。
For a group $G$ and $ω\in Z^{3}(G, \text{U}(1))$, an $ω$-anomalous action on a C*-algebra $B$ is a $\text{U}(1)$-linear monoidal functor between 2-groups $\text{2-Gr}(G, \text{U}(1), ω)\rightarrow \underline{\text{Aut}}(B)$, where the latter denotes the 2-group of $*$-automorphisms of $B$. The class $[ω]\in H^{3}(G, \text{U}(1))$ is called the anomaly of the action. We show for every $n\ge 2$ and every finite group $G$, every anomaly can be realized on the stabilization of a commutative C*-algebra $C(M)\otimes \mathcal{K}$ for some closed connected $n$-manifold $M$. We also show that although there are no anomalous symmetries of Roe C*-algebras of coarse spaces, for every finite group $G$, every anomaly can be realized on the Roe corona $C^{*}(X)/\mathcal{K}$ of some bounded geometry metric space $X$ with property $A$.
