Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the connectedness of spectral sets and irreducibility of spectral
  cones in Euclidean Jordan algebras   Let V be a Euclidean Jordan algebra of rank n. The eigenvalue map from V to
R^n takes any element x in V to the vector of eigenvalues of x written in the
decreasing order. A spectral set in V is the inverse image of a permutation set
in R^n under the eigenvalue map. If the permutation set is also a convex cone,
the spectral set is said to be a spectral cone. This paper deals with
connectedness and arcwise connectedness properties of spectral sets. By relying
on the result that in a simple Euclidean Jordan algebra, every eigenvalue orbit
is arcwise connected, we show that if a permutation invariant set is connected
(arcwise connected), then the corresponding spectral set is connected
(respectively, arcwise connected). A related result is that in a simple
Euclidean Jordan algebra, every pointed spectral cone is irreducible.

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The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
16
The categories of this paper are: stat
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The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
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The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci