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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/145604It 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.26 pagesQuantum AlgebraRepresentation Theory14M99, 16G20, 16G70Green's formula with $\bbc^{*}$-action and Caldero-Keller's formula for cluster algebrastext