6 papers
Quantum cluster variables via canonical submodules
Fan Xu, Yutong Yu
We study quantum cluster algebras from marked surfaces without punctures. We express the quantum cluster variables in terms of the canonical submodules. As a byproduct, we obtain t…
Enveloping algebras via motivic Hall algebras
Xinyi Feng, Fan Xu
We give a geometric realization of the whole universal enveloping algebra of the Borcherds-Bozec algebra using quiver with loops via the motivic semi-derived Hall algebra approach.…
Stability Conditions and Harder-Narasimhan Filtrations for Triangulated Categories
Wenyu Gao, Fan Xu
In this paper, we investigate the relationships between Harder-Narasimhan filtrations and derived Hall algebras. We extend several results from abelian categories to triangulated c…
Fundamental relations in quantum cluster algebras
Junyuan Huang, Xueqing Chen, Ming Ding +1
Let be an arbitrary quantum cluster algebra with principal coefficients. We give the fundamental relations between the quantum cluster variables arising from one-…
Explicit cluster multiplication formulas for the quantum cluster algebra of type
Danting Yang, Xueqing Chen, Ming Ding +1
Let be an affine quiver of type . We explicitly construct the cluster multiplication formulas for the quantum cluster algebra of with principal coefficients. As…
On the acyclic quantum cluster algebras with principal coefficients
Junyuan Huang, Xueqing Chen, Ming Ding +1
In this paper, we focus on a new lower bound quantum cluster algebra which is generated by the initial quantum cluster variables and the quantum projective cluster variables of an…