2 citations · 3 across the 6 of their papers we have counts for
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Lie algebras arising from 1-cyclic perfect complexes
Shiquan Ruan, Jie Sheng, Haicheng Zhang
Let be the path algebra of a Dynkin quiver over a finite field, and be the category of projective -modules. Denote by the category of 1-…
An insight into the description of the crystal structure for Mirković-Vilonen polytopes
Yong Jiang, Jie Sheng
We study the description of the crystal structure on the set of Mirković-Vilonen polytopes. Anderson and Mirković defined an operator and conjectured that it coincides with the Kas…
Multiplicative properties of a quantum Caldero-Chapoton map associated to valued quivers
Ming Ding, Jie Sheng
We prove a multiplication theorem of a quantum Caldero-Chapoton map associated to valued quivers which extends the results in \cite{DX}\cite{D}. As an application, when is a va…
Complex Lie algebras corresponding to weighted projective lines
Rujing Dou, Jie Sheng, Jie Xiao
The aim of this paper is to give an alternative proof of Kac's theorem for weighted projective lines (\cite{W}) over the complex field. The geometric realization of complex Lie alg…
Tame quivers and affine enveloping algebras
Yong Jiang, Jie Sheng
Let be an affine Kac-Moody algebra with symmetric Cartan datum, be the maximal nilpotent subalgebra of . By the Hall algebra approac…
The elements in crystal bases corresponding to exceptional modules
Yong Jiang, Jie Sheng, Jie Xiao
According to the Ringel-Green Theorem([G],[R1]), the generic composition algebra of the Hall algebra provides a realization of the positive part of the quantum group. Furthermore,…