A generalized quantum cluster algebra of Kronecker type-Reference-Cited by-同舟云学术

A generalized quantum cluster algebra of Kronecker type

Published:2024 Issue:1 Volume:32 Page:670-685
ISSN:2688-1594
Container-title:Electronic Research Archive
language:
Short-container-title:era

Author:

Bai Liqian¹,Chen Xueqing²,Ding Ming³,Xu Fan⁴

Affiliation:

1. Department of Applied Mathematics, Northwestern Polytechnical University, Shaanxi 710072, China

2. Department of Mathematics, University of Wisconsin-Whitewater, Whitewater WI.53190, USA

3. School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China

4. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China

Abstract

<abstract><p>The notion of generalized quantum cluster algebras was introduced as a natural generalization of Berenstein and Zelevinsky's quantum cluster algebras as well as Chekhov and Shapiro's generalized cluster algebras. In this paper, we focus on a generalized quantum cluster algebra of Kronecker type which possesses infinitely many cluster variables. We obtain the cluster multiplication formulas for this algebra. As an application of these formulas, a positive bar-invariant basis is explicitly constructed. Both results generalize those known for the Kronecker cluster algebra and quantum cluster algebra.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference24 articles.

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