Anomalous symmetries of classifiable C*-algebras

被引：2

作者：

Evington, Samuel ^{[1
]}

Pacheco, Sergio ^{[1
,2
]}

机构：

[1] Univ Munster, Math Inst, Einsteinstr 62, D-48149 Munster, Germany

[2] Univ Oxford, Math Inst, Oxford OX2 6GG, England

来源：

STUDIA MATHEMATICA | 2023年 / 270卷 / 01期

基金：

美国国家科学基金会; 欧洲研究理事会; 英国工程与自然科学研究理事会;

关键词：

classification of C-?-algebras; quantum symmetries; FINITE WATATANI INDEXES; MORITA EQUIVALENCE; CROSSED-PRODUCTS; CLASSIFICATION; REPRESENTATIONS; AUTOMORPHISMS; SUBALGEBRAS; SUBFACTORS; BIMODULES; PROPERTY;

D O I：

10.4064/sm220117-25-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the H3 invariant of a group homomorphism phi : G -> Out(A), where A is a classifiable C*-algebra. We show the existence of an obstruction to possible H3 invariants arising from considering the unitary algebraic K1-group. In particular, we prove that when A is the Jiang-Su algebra Z this invariant must vanish. We deduce that the unitary fusion categories Hilb(G, omega) for non-trivial omega is an element of H3(G, T) cannot act on Z.

引用

页码：73 / 102

页数：30

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