Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Curious properties of free hypergraph C*-algebras   A finite hypergraph $H$ consists of a finite set of vertices $V(H)$ and a
collection of subsets $E(H) \subseteq 2^{V(H)}$ which we consider as partition
of unity relations between projection operators. These partition of unity
relations freely generate a universal C*-algebra, which we call the "free
hypergraph C*-algebra" $C^*(H)$. General free hypergraph C*-algebras were first
studied in the context of quantum contextuality. As special cases, the class of
free hypergraph C*-algebras comprises quantum permutation groups, maximal group
C*-algebras of graph products of finite cyclic groups, and the C*-algebras
associated to quantum graph homomorphism, isomorphism, and colouring.
  Here, we conduct the first systematic study of aspects of free hypergraph
C*-algebras. We show that they coincide with the class of finite colimits of
finite-dimensional commutative C*-algebras, and also with the class of
C*-algebras associated to synchronous nonlocal games. We had previously shown
that it is undecidable to determine whether $C^*(H)$ is nonzero for given $H$.
We now show that it is also undecidable to determine whether a given $C^*(H)$
is residually finite-dimensional, and similarly whether it only has
infinite-dimensional representations, and whether it has a tracial state. It
follows that for each one of these properties, there is $H$ such that the
question whether $C^*(H)$ has this property is independent of the ZFC axioms,
assuming that these are consistent. We clarify some of the subtleties
associated with such independence results in an appendix.

9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat