Anomalous symmetries of classifiable C*-algebras

IF 0.7 3区 数学 Q2 MATHEMATICS
Samuel Evington, Sergio Gir'on Pacheco
{"title":"Anomalous symmetries of classifiable C*-algebras","authors":"Samuel Evington, Sergio Gir'on Pacheco","doi":"10.4064/sm220117-25-6","DOIUrl":null,"url":null,"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 $\\mathcal{Z}$.","PeriodicalId":51179,"journal":{"name":"Studia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2021-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Studia Mathematica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4064/sm220117-25-6","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
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。
求助全文
约1分钟内获得全文 求助全文
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.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信