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：
欧洲研究理事会; 美国国家科学基金会; 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.
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页码：73 / 102
页数：30
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