Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algebraically irreducible representations and structure space of the
  Banach algebra associated with a topological dynamical system   If $X$ is a compact Hausdorff space and $\sigma$ is a homeomorphism of $X$,
then a Banach algebra $\ell^1(\Sigma)$ of crossed product type is naturally
associated with this topological dynamical system $\Sigma=(X,\sigma)$. If $X$
consists of one point, then $\ell^1(\Sigma)$ is the group algebra of the
integers.
  We study the algebraically irreducible representations of $\ell^1(\Sigma)$ on
complex vector spaces, its primitive ideals and its structure space. The finite
dimensional algebraically irreducible representations are determined up to
algebraic equivalence, and a sufficiently rich family of infinite dimensional
algebraically irreducible representations is constructed to be able to conclude
that $\ell^1(\Sigma)$ is semisimple. All primitive ideals of $\ell^1(\Sigma)$
are selfadjoint, and $\ell^1(\Sigma)$ is Hermitian if there are only periodic
points in $X$. If $X$ is metrisable or all points are periodic, then all
primitive ideals arise as in our construction. A part of the structure space of
$\ell^1(\Sigma)$ is conditionally shown to be homeomorphic to the product of a
space of finite orbits and $\mathbb T$. If $X$ is a finite set, then the
structure space is the topological disjoint union of a number of tori, one for
each orbit in $X$. If all points of $X$ have the same finite period, then it is
the product of the orbit space $X/\mathbb Z$ and $\mathbb T$. For rational
rotations of $\mathbb T$, this implies that the structure space is homeomorphic
to $\mathbb T^2$.

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The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th