Green's formula with *-action and Caldero-Keller's formula for cluster algebras
Abstract
It is known that Green's formula over finite fields gives rise to the comultiplications of Ringel-Hall algebras and quantum groups (seeGreen, also see Lusztig). In this paper, we deduce the projective version of Green's formula in a geometric way. Then following the method of Hubery in Hubery2005, we apply this formula to proving Caldero-Keller's multiplication formula for acyclic cluster algebras of arbitrary type.
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