Anomalous symmetries of classifiable C*-algebras

IF 0.7 3区 数学 Q2 MATHEMATICS
Samuel Evington, Sergio Gir'on Pacheco
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引用次数: 5

Abstract

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 $\mathcal{Z}$.
可分类C*-代数的异常对称性
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$\mathcal{Z}$。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Studia Mathematica
Studia Mathematica 数学-数学
CiteScore
1.50
自引率
12.50%
发文量
72
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.
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