Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equivariant property (SI) revisited   We revisit Matui-Sato's notion of property (SI) for C*-algebras and
C*-dynamics. More specifically, we generalize the known framework to the case
of C*-algebras with possibly unbounded traces. The novelty of this approach
lies in the equivariant context, where none of the previous work allows one to
(directly) apply such methods to actions of amenable groups on highly
non-unital C*-algebras, in particular to establish equivariant Jiang-Su
stability. Our main result is an extension of an observation by Sato: For any
countable amenable group $\Gamma$ and any non-elementary separable simple
nuclear C*-algebra $A$ with strict comparison, every $\Gamma$-action on $A$ has
equivariant property (SI). A more general statement involving relative property
(SI) for inclusions into ultraproducts is proved as well. As a consequence we
show that if $A$ also has finitely many rays of extremal traces, then every
$\Gamma$-action on $A$ is equivariantly Jiang-Su stable. We moreover provide
applications of the main result to the context of strongly outer actions, such
as a generalization of Nawata's classification of strongly outer automorphisms
on the (stabilized) Razak-Jacelon algebra.

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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
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The categories of this paper are: q-fin