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math.QA2007★ 3 cited
Representations of tame quivers and affine canonical bases
Zongzhu Lin, Jie Xiao, Guanglian Zhang
An integral PBW-basis of type has been constructed by Zhang [Z] and Chen [C] using the Auslander-Reiten quiver of the Kronecker quiver. We associate a geometric order t…
math.QA2007
Green's formula with $\bbc^{*}$-action and Caldero-Keller's formula for cluster algebras
Jie Xiao, Fan Xu
It 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 th…