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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Final published version
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
}
TY - JOUR
T1 - Graded quantum cluster algebras of infinite rank as colimits
AU - Grabowski, Jan E.
AU - Gratz, Sira
N1 - 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
PY - 2018/11
Y1 - 2018/11
N2 - 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.
AB - 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.
KW - math.QA
KW - math.RT
KW - 13F60
U2 - 10.1016/j.jpaa.2017.12.014
DO - 10.1016/j.jpaa.2017.12.014
M3 - Journal article
VL - 222
SP - 3395
EP - 3413
JO - Journal of Pure and Applied Algebra
JF - Journal of Pure and Applied Algebra
SN - 0022-4049
IS - 11
ER -