Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $K$-theory for real $k$-graph $C^*$-algebras   We initiate the study of real $C^*$-algebras associated to higher-rank graphs
$\Lambda$, with a focus on their $K$-theory. Following Kasparov and Evans, we
identify a spectral sequence which computes the $\mathcal{CR}$ $K$-theory of
$C^*_{\mathbb R} (\Lambda, \gamma)$ for any involution $\gamma$ on $\Lambda$,
and show that the $E^2$ page of this spectral sequence can be straightforwardly
computed from the combinatorial data of the $k$-graph $\Lambda$ and the
involution $\gamma$. We provide a complete description of $K^{CR}(C^*_{\mathbb
R}(\Lambda, \gamma))$ for several examples of higher-rank graphs $\Lambda$ with
involution.

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The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex