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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