Green's formula with $\bbc^{*}$-action and Caldero-Keller's formula for cluster algebras

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dc.creatorXiao, Jie
dc.creatorXu, Fan
dc.date2007-07-09
dc.date2008-01-10
dc.date.accessioned2026-07-07T08:53:23Z
dc.date.available2026-07-07T08:53:23Z
dc.descriptionIt is known that Green's formula over finite fields gives rise to the comultiplications of Ringel-Hall algebras and quantum groups (see\cite{Green}, also see \cite{Lusztig}). In this paper, we deduce the projective version of Green's formula in a geometric way. Then following the method of Hubery in \cite{Hubery2005}, we apply this formula to proving Caldero-Keller's multiplication formula for acyclic cluster algebras of arbitrary type.
dc.description26 pages
dc.identifierhttps://arxiv.org/abs/0707.1175
dc.identifierhttp://arxiv.org/abs/0707.1175
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/145604
dc.subjectQuantum Algebra
dc.subjectRepresentation Theory
dc.subject14M99, 16G20, 16G70
dc.titleGreen's formula with $\bbc^{*}$-action and Caldero-Keller's formula for cluster algebras
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