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<identifier>oai:HAL:hal-00821878v1</identifier>
<datestamp>2018-01-11</datestamp>
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<setSpec>subject:math</setSpec>
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<setSpec>collection:CNRS</setSpec>
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<publisher>HAL CCSD</publisher>
<title lang=fr>Quasi-cluster algebras from non-orientable surfaces</title>
<creator>Dupont, Grégoire</creator>
<creator>Palesi, Frédéric</creator>
<contributor>École supérieure du professorat et de l'éducation - Guadeloupe (ESPE Guadeloupe) ; Université des Antilles et de la Guyane (UAG)</contributor>
<contributor>Institut de Mathématiques de Marseille (I2M) ; Aix Marseille Université (AMU) - Ecole Centrale de Marseille (ECM) - Centre National de la Recherche Scientifique (CNRS)</contributor>
<description>44 pages, 14 figures</description>
<description>International audience</description>
<source>ISSN: 0925-9899</source>
<source>EISSN: 1572-9192</source>
<source>Journal of Algebraic Combinatorics</source>
<publisher>Springer Verlag</publisher>
<identifier>hal-00821878</identifier>
<identifier>https://hal.archives-ouvertes.fr/hal-00821878</identifier>
<source>https://hal.archives-ouvertes.fr/hal-00821878</source>
<source>Journal of Algebraic Combinatorics, Springer Verlag, 2015, pp.10.1007. 〈10.1007/s10801-015-0586-1〉</source>
<identifier>ARXIV : 1105.1560</identifier>
<relation>info:eu-repo/semantics/altIdentifier/arxiv/1105.1560</relation>
<identifier>DOI : 10.1007/s10801-015-0586-1</identifier>
<relation>info:eu-repo/semantics/altIdentifier/doi/10.1007/s10801-015-0586-1</relation>
<language>en</language>
<subject lang=en>hyperbolic geometry</subject>
<subject lang=en>non-orientable surfaces</subject>
<subject lang=en>triangulation of surfaces</subject>
<subject lang=en>cluster algebras</subject>
<subject>[MATH.MATH-RA] Mathematics [math]/Rings and Algebras [math.RA]</subject>
<subject>[MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT]</subject>
<type>info:eu-repo/semantics/article</type>
<type>Journal articles</type>
<description lang=en>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.</description>
<date>2015</date>
</dc>
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