Anomalous symmetries of classifiable C*-algebras

2021/05/12 by Evington, Samuel, Pacheco, Sergio Girón · 2 citations
#46L35 (Primary) 46L37 (Secondary) #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2105.05587

Abstract

We study the H³ invariant of a group homomorphism ϕ: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, ω) for non-trivial ω∈ H³(G, \mathbbT) cannot act on Z.

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• Properly Outer Actions of Tensor Categories on C^*-algebras
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