Graded quantum cluster algebras of infinite rank as colimits

Grabowski, J. E. and Gratz, S. (2018) Graded quantum cluster algebras of infinite rank as colimits. Journal of Pure and Applied Algebra, 222(11), pp. 3395-3413. (doi:10.1016/j.jpaa.2017.12.014)

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Abstract

We provide a graded and quantum version of the category of rooted cluster algebras introduced by Assem, Dupont and Schiffler and show that every graded quantum cluster algebra of infinite rank can be written as a colimit of graded quantum cluster algebras of finite rank. As an application, for each k we construct a graded quantum infinite Grassmannian admitting a cluster algebra structure, extending an earlier construction of the authors for k=2.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Gratz, Dr Sira
Authors: Grabowski, J. E., and Gratz, S.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Journal of Pure and Applied Algebra
Publisher:Elsevier
ISSN:0022-4049
ISSN (Online):1873-1376
Published Online:23 December 2017
Copyright Holders:Copyright © 2017 Elsevier B.V.
First Published:First published in Journal of Pure and Applied Algebra 222(11): 3395-3413
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher.

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