The cluster multiplication theorem for acyclic quantum cluster algebras
Representation Theory
2021-11-19 v2 Quantum Algebra
Rings and Algebras
Abstract
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 quotients of derived Hall subalgebras of . These formulas can be viewed as the quantum version of the cluster multiplication theorem in the classical cluster algebra proved by Caldero-Keller for finite type, Hubery for affine type and Xiao-Xu for acyclic quivers.
Cite
@article{arxiv.2108.03558,
title = {The cluster multiplication theorem for acyclic quantum cluster algebras},
author = {Xueqing Chen and Ming Ding and Haicheng Zhang},
journal= {arXiv preprint arXiv:2108.03558},
year = {2021}
}
Comments
34 pages; Change the original title and add an example