The Cluster Multiplication Theorem for Acyclic Quantum Cluster Algebras-Reference-Cited by-同舟云学术

The Cluster Multiplication Theorem for Acyclic Quantum Cluster Algebras

Published:2023-07-25 Issue:23 Volume:2023 Page:20533-20573
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Chen Xueqing¹,Ding Ming²,Zhang Haicheng³

Affiliation:

1. Department of Mathematics, University of Wisconsin–Whitewater , 800 W. Main Street, Whitewater, WI 53190, USA

2. School of Mathematics and Information Science, Guangzhou University , Guangzhou 510006, P. R. China

3. Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University , Nanjing 210023, P. R. China

Abstract

Abstract Let $Q$ be a finite acyclic valued quiver. We give the cluster multiplication formulas in the quantum cluster algebra of $Q$ with arbitrary coefficients, by applying certain quotients of derived Hall subalgebras of $Q$. 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.

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

https://academic.oup.com/imrn/article-pdf/2023/23/20533/54019892/rnad172.pdf

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