Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Group actions on simple tracially $\mathcal{Z}$-absorbing C*-algebras   We show that if $A$ is a simple (not necessarily unital) tracially
$\mathcal{Z}$-absorbing C*-algebra and $\alpha \colon G \to \mathrm{Aut} (A)$
is an action of a finite group $G$ on $A$ with the weak tracial Rokhlin
property, then the crossed product $C^*(G, A,\alpha)$ and the fixed point
algebra $A^\alpha$ are simple and tracially $\mathcal{Z}$-absorbing, and they
are $\mathcal{Z}$-stable if, in addition, $A$ is separable and nuclear. The
same conclusion holds for all intermediate C*-algebras of the inclusions
$A^\alpha \subseteq A$ and $A \subseteq C^*(G, A,\alpha)$. We prove that if $A$
is a simple tracially $\mathcal{Z}$-absorbing C*-algebra, then, under a
finiteness condition, the permutation action of the symmetric group $S_m$ on
the minimal $m$-fold tensor product of $A$ has the weak tracial Rokhlin
property. We define the weak tracial Rokhlin property for automorphisms of
simple C*-algebras and we show that -- under a mild assumption -- (tracial)
$\mathcal{Z}$-absorption is preserved under crossed products by such
automorphisms.

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The categories of this paper are: adap-org
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The categories of this paper are: cond-mat
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The categories of this paper are: econ
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: gr-qc
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph