可分类C*-代数的异常对称性

IF 0.7 3区数学 Q2 MATHEMATICS

Studia Mathematica Pub Date : 2021-05-12 DOI:10.4064/sm220117-25-6

Samuel Evington, Sergio Gir'on Pacheco

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引用次数: 5

摘要

我们研究了群同态$\phi:G\rightarrow\mathrm{Out}（a）$的$H^3$不变量，其中$a$是可分类的C$^*$-代数。我们证明了由考虑酉代数$K_1$群引起的可能的$H^3$不变量的障碍的存在性。特别地，我们证明了当$A$是姜代数$\mathcal{Z}$时，这个不变量必须消失。我们推导出H^3（G，\mathbb｛T｝）$中非平凡$\omega的酉融合范畴$\mathrm｛Hilb｝（G，\omega）$不能作用于$\mathcal｛Z｝$。

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Anomalous symmetries of classifiable C*-algebras

We study the $H^3$ invariant of a group homomorphism $\phi:G \rightarrow \mathrm{Out}(A)$, where $A$ is a classifiable C$^*$-algebra. We show the existence of an obstruction to possible $H^3$ invariants arising from considering the unitary algebraic $K_1$ group. In particular, we prove that when $A$ is the Jiang--Su algebra $\mathcal{Z}$ this invariant must vanish. We deduce that the unitary fusion categories $\mathrm{Hilb}(G, \omega)$ for non-trivial $\omega \in H^3(G, \mathbb{T})$ cannot act on $\mathcal{Z}$.

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来源期刊

Studia Mathematica 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

审稿时长

5 months

期刊介绍： The journal publishes original papers in English, French, German and Russian, mainly in functional analysis, abstract methods of mathematical analysis and probability theory.