Graded quantum cluster algebras of infinite rank as colimits
Quantum Algebra
2015-10-15 v1 Representation Theory
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.
Keywords
Cite
@article{arxiv.1510.04109,
title = {Graded quantum cluster algebras of infinite rank as colimits},
author = {Jan E. Grabowski and Sira Gratz},
journal= {arXiv preprint arXiv:1510.04109},
year = {2015}
}
Comments
18 pages, 1 figure