scholarly journals The Berenstein–Zelevinsky quantum cluster algebra conjecture

2020 ◽  
Vol 22 (8) ◽  
pp. 2453-2509 ◽  
Author(s):  
Kenneth Goodearl ◽  
M. T. Yakimov
Keyword(s):  
Cluster Algebra ◽  
Quantum Cluster Algebra ◽  
Quantum Cluster

scholarly journals Bar-invariant bases of the quantum cluster algebra of type A 2 (2)

2011 ◽  
Vol 61 (4) ◽  
pp. 1077-1090 ◽  
Author(s):  
Xueqing Chen ◽  
Ming Ding ◽  
Jie Sheng
Keyword(s):  
Cluster Algebra ◽  
Type A ◽  
Quantum Cluster Algebra ◽  
Quantum Cluster

scholarly journals Braiding operator via quantum cluster algebra

2014 ◽  
Vol 47 (47) ◽  
pp. 474006 ◽  
Author(s):  
Kazuhiro Hikami ◽  
Rei Inoue
Keyword(s):  
Cluster Algebra ◽  
Quantum Cluster Algebra ◽  
Quantum Cluster

scholarly journals A quantum cluster algebra approach to representations of simply laced quantum affine algebras

2020 ◽  
Author(s):  
Léa Bittmann
Keyword(s):  
Cluster Algebra ◽  
Irreducible Representations ◽  
Algebra Structure ◽  
Quantum Affine Algebra ◽  
Affine Algebra ◽  
Grothendieck Ring ◽  
Finite Dimensional ◽  
Quantum Cluster Algebra ◽  
Algebra Approach ◽  
Quantum Cluster

AbstractWe establish a quantum cluster algebra structure on the quantum Grothendieck ring of a certain monoidal subcategory of the category of finite-dimensional representations of a simply-laced quantum affine algebra. Moreover, the (q, t)-characters of certain irreducible representations, among which fundamental representations, are obtained as quantum cluster variables. This approach gives a new algorithm to compute these (q, t)-characters. As an application, we prove that the quantum Grothendieck ring of a larger category of representations of the Borel subalgebra of the quantum affine algebra, defined in a previous work as a quantum cluster algebra, contains indeed the well-known quantum Grothendieck ring of the category of finite-dimensional representations. Finally, we display our algorithm on a concrete example.

Cluster multiplication theorem in the quantum cluster algebra of type A2(2) and the triangular basis

2019 ◽  
Vol 533 ◽  
pp. 106-141
Author(s):  
Liqian Bai ◽  
Xueqing Chen ◽  
Ming Ding ◽  
Fan Xu
Keyword(s):  
Cluster Algebra ◽  
Quantum Cluster Algebra ◽  
Quantum Cluster ◽  
Multiplication Theorem
Sign in / Sign up

Export Citation Format

Share Document