Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ground states of groupoid C*-algebras, phase transitions and arithmetic
  subalgebras for Hecke algebras   We consider the Hecke pair consisting of the group $P^+_K$ of affine
transformations of a number field $K$ that preserve the orientation in every
real embedding and the subgroup $P^+_O$ consisting of transformations with
algebraic integer coefficients. The associated Hecke algebra $C^*(P^+_K,P^+_O)$
has a natural time evolution $\sigma$, and we describe the corresponding phase
transition for KMS$_\beta$-states and for ground states. From work of
Yalkinoglu and Neshveyev it is known that a Bost-Connes type system associated
to $K$ has an essentially unique arithmetic subalgebra. When we import this
subalgebra through the isomorphism of $C^*(P^+_K,P^+_O)$ to a corner in the
Bost-Connes system established by Laca, Neshveyev and Trifkovic, we obtain an
arithmetic subalgebra of $C^*(P^+_K,P^+_O)$ on which ground states exhibit the
`fabulous' property with respect to an action of the Galois group
$Gal(K^{ab}/H_+(K))$, where $H_+(K)$ is the narrow Hilbert class field.
  In order to characterize the ground states of the $C^*$-dynamical system
$(C^*(P^+_K,P^+_O),\sigma)$, we obtain first a characterization of the ground
states of a groupoid $C^*$-algebra, refining earlier work of Renault. This is
independent from number theoretic considerations, and may be of interest by
itself in other situations.

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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: q-bio
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The categories of this paper are: cs
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ph
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The categories of this paper are: econ
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The categories of this paper are: plasm-ph
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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: adap-org