Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Triviality of Equivariant Maps in Crossed Products and Matrix Algebras   We consider a "twisted" noncommutative join procedure for unital
$C^*$-algebras which admit actions by a compact abelian group $G$ and its
discrete abelian dual $\Gamma$, so that we may investigate an analogue of
Baum-Dabrowski-Hajac noncommutative Borsuk-Ulam theory in the twisted setting.
Namely, under what conditions is it guaranteed that an equivariant map $\phi$
from a unital $C^*$-algebra $A$ to the twisted join of $A$ and $C^*(\Gamma)$
cannot exist? This pursuit is motivated by the twisted analogues of even
spheres, which admit the same $K_0$ groups as even spheres and have an
analogous Borsuk-Ulam theorem that is detected by $K_0$, despite the fact that
the objects are not themselves deformations of a sphere. We find multiple
sufficient conditions for twisted Borsuk-Ulam theorems to hold, one of which is
the addition of another equivariance condition on $\phi$ that corresponds to
the choice of twist. However, we also find multiple examples of equivariant
maps $\phi$ that exist even under fairly restrictive assumptions. Finally, we
consider an extension of unital contractibility (in the sense of
Dabrowski-Hajac-Neshveyev) "modulo $k$."

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The categories of this paper are: funct-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
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The categories of this paper are: physics
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The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: astro-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: quant-ph