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  • Grabowski-Gratz-Graded-Quantum-Colimits-JPAA-final

    Rights statement: 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

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Graded quantum cluster algebras of infinite rank as colimits

Research output: Contribution to journalJournal article

Published
<mark>Journal publication date</mark>11/2018
<mark>Journal</mark>Journal of Pure and Applied Algebra
Issue number11
Volume222
Number of pages18
Pages (from-to)3395-3413
Publication statusPublished
Early online date23/12/17
Original languageEnglish

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.

Bibliographic note

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