Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quasi-cluster algebras from non-orientable surfaces   With any non necessarily orientable unpunctured marked surface (S,M) we
associate a commutative algebra, called quasi-cluster algebra, equipped with a
distinguished set of generators, called quasi-cluster variables, in bijection
with the set of arcs and one-sided simple closed curves in (S,M). Quasi-cluster
variables are naturally gathered into possibly overlapping sets of fixed
cardinality, called quasi-clusters, corresponding to maximal non-intersecting
families of arcs and one-sided simple closed curves in (S,M). If the surface S
is orientable, then the quasi-cluster algebra is the cluster algebra associated
with the marked surface (S,M) in the sense of Fomin, Shapiro and Thurston. We
classify quasi-cluster algebras with finitely many quasi-cluster variables and
prove that for these quasi-cluster algebras, quasi-cluster monomials form a
linear basis. Finally, we attach to (S,M) a family of discrete integrable
systems satisfied by quasi-cluster variables associated to arcs in the
quasi-cluster algebra and we prove that solutions of these systems can be
expressed in terms of cluster variables of type A.

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The categories of this paper are: physics
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The categories of this paper are: gr-qc
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The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-ex
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The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: eess
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: q-bio