17 citations · 154 across the 69 of their papers we have counts for
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The Multiplication Formulas of Weighted Quantum Cluster Functions
Zhimin Chen, Jie Xiao, Fan Xu
By applying the property of Ext-symmetry and the affine space structure of certain fibers, we introduce the notion of weighted quantum cluster functions and prove their multiplicat…
Hall algebras of cyclic quivers and -deformed Fock spaces
Bangming Deng, Jie Xiao
Based on the work of Ringel and Green, one can define the (Drinfeld) double Ringel--Hall algebra of a quiver as well as its highest weight modules. The main p…
Remarks on Hall algebras of triangulated categories
Jie Xiao, Fan Xu
We introduce the notion of the Drinfeld dual of an algebra and show that Hall algebras defined by Kontsevich-Soibelman in \cite{KS} are the Drinfeld duals of derived Hall algebras…
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…
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…
Hall algebras associated to triangulated categories
Jie Xiao, Fan Xu
By counting with triangles and the octohedral axiom, we find a direct way to prove the formula of Toën in \cite{Toen2005} for a triangulated category with (left) homological-finite…
Derived Categories and Lie Algebras
Jie Xiao, Fan Xu, Guanglian Zhang
Let $\md^b(A)$ be the derived category of a finite dimensional basic algebra with finite global dimension. We construct the Lie algebra arising from the 2-periodic version $\mk…
Realizing Enveloping Algebras via Varieties of Modules
Ming Ding, Jie Xiao, Fan Xu
By using the Ringel-Hall algebra approach, we investigate the structure of the Lie algebra generated by indecomposable constructible sets in the varieties of modules for any…