3 citations · 5 across the 17 of their papers we have counts for
17 papers
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…
Some properties of generalized cluster algebras of geometric types
Junyuan Huang, Xueqing Chen, Fan Xu +1
We study the lower bound algebras generated by the generalized projective cluster variables of acyclic generalized cluster algebras of geometric types. We prove that this lower bou…
On a conjecture of transposed Poisson -Lie algebras
Junyuan Huang, Xueqing Chen, Zhiqi Chen +1
In this paper, we obtain a rich family of identities for transposed Poisson -Lie algebras, and then prove the conjecture of Bai, Bai, Guo and Wu in \cite{BBGW} under certain str…
A generalized quantum cluster algebra of Kronecker type
Liqian Bai, Xueqing Chen, Ming Ding +1
The cluster multiplication formulas for a generalized quantum cluster algebra of Kronecker type are explicitly given. Furthermore, a positive bar-invariant $\mathbb{Z}[q^{\pm\frac{…
Generalized quantum cluster algebras: the Laurent phenomenon and upper bounds
Liqian Bai, Xueqing Chen, Ming Ding +1
Generalized quantum cluster algebras introduced in [1] are quantum deformation of generalized cluster algebras of geometric types. In this paper, we prove that the Laurent phenomen…
Recursive formulas for the Kronecker quantum cluster algebra with principal coefficients
Ming Ding, Fan Xu, Xueqing Chen
We use the quantum version of Chebyshev polynomials to explicitly construct the recursive formulas for the Kronecker quantum cluster algebra with principal coefficients. As a bypro…
The cluster multiplication theorem for acyclic quantum cluster algebras
Xueqing Chen, Ming Ding, Haicheng Zhang
Let be a finite acyclic valued quiver. We give the cluster multiplication formulas in the quantum cluster algebra of with arbitrary coefficients, by applying certain quotie…
Atomic basis of quantum cluster algebra of type
Ming Ding, Fan Xu, Xueqing Chen
Let be the affine quiver of type and be the quantum cluster algebra associated to the valued quiver . We prove…
On the Generalized Cluster Algebras of Geometric Type
Liqian Bai, Xueqing Chen, Ming Ding +1
We develop and prove the analogs of some results shown in [Berenstein A., Fomin S., Zelevinsky A., Duke Math. J. 126 (2005), 1-52] concerning lower and upper bounds of cluster alge…
Cluster multiplication theorem in the quantum cluster algebra of type
Liqian Bai, Xueqing Chen, Ming Ding +1
The objective of the present paper is to prove cluster multiplication theorem in the quantum cluster algebra of type . As corollaries, we obtain bar-invariant $\mathbb…
A quantum analogue of generalized cluster algebras
Liqian Bai, Xueqing Chen, Ming Ding +1
We define a quantum analogue of a class of generalized cluster algebras which can be viewed as a generalization of quantum cluster algebras defined in \cite{berzel}. In the case of…
On positivity for generalized cluster variables of affine quivers
Xueqing Chen, Ming Ding, Fan Xu
It has been proved in \cite{LS} that cluster variables in cluster algebras of every skew-symmetric cluster algebra are positive. We prove that any regular generalized cluster varia…
Fermionic Novikov algebras admitting invariant non-degenerate symmetric bilinear forms are Novikov algebras
Zhiqi Chen, Ming Ding
This paper is to prove that a fermionic Novikov algebra equipped with an invariant non-degenerate symmetric bilinear form is a Novikov algebra.
On homomorphisms from Ringel-Hall algebras to quantum cluster algebras
Xueqing Chen, Ming Ding, Fan Xu
In \cite{rupel3},the authors defined algebra homomorphisms from the dual Ringel-Hall algebra of certain hereditary abelian category to an appropriate -polynomial a…
Hall algebras for odd periodic triangulated categories
Fan Xu, Xueqing Chen
We define the Hall algebra associated to any triangulated category under some finiteness conditions with the -periodic translation functor for odd This generalizes th…