F-polynomials in Quantum Cluster Algebras

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dc.creatorTran, Thao
dc.date2009-04-21
dc.date.accessioned2026-07-07T13:06:54Z
dc.date.available2026-07-07T13:06:54Z
dc.descriptionF-polynomials and g-vectors were defined by Fomin and Zelevinsky to give a formula which expresses cluster variables in a cluster algebra in terms of the initial cluster data. A quantum cluster algebra is a certain noncommutative deformation of a cluster algebra. In this paper, we define and prove the existence of analogous quantum F-polynomials for quantum cluster algebras. We prove some properties of quantum F-polynomials. In particular, we give a recurrence relation which can be used to compute them. Finally, we compute quantum F-polynomials and g-vectors for a certain class of cluster variables, which includes all cluster variables in type A quantum cluster algebras.
dc.description36 pages, 1 figure
dc.identifierhttps://arxiv.org/abs/0904.3291
dc.identifierhttp://arxiv.org/abs/0904.3291
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/227927
dc.subjectRings and Algebras
dc.subjectCombinatorics
dc.subjectRepresentation Theory
dc.subject16S99 (Primary), 05E15, 20G42 (Secondary)
dc.titleF-polynomials in Quantum Cluster Algebras
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