Graded quantum cluster algebras of infinite rank as colimits

Grabowski, Jan E. and Gratz, Sira (2018) Graded quantum cluster algebras of infinite rank as colimits. Journal of Pure and Applied Algebra, 222 (11). pp. 3395-3413. ISSN 0022-4049

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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:
Journal Article
Journal or Publication Title:
Journal of Pure and Applied Algebra
Additional Information:
This is the author’s version of a work that was accepted for publication in Journal of Pure and Applied Algebra. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Pure and Applied Algebra, 222, (11), 2018 DOI: 10.1016/j.jpaa.2017.12.014
Uncontrolled Keywords:
?? math.qamath.rt13f60algebra and number theory ??
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Deposited On:
04 Feb 2016 13:28
Last Modified:
27 Apr 2024 23:48