Monoidal categorification of cluster algebras
Abstract
We give a definition of monoidal categorifications of quantum cluster algebras and provide a criterion for a monoidal category of finitedimensional graded $R$modules to become a monoidal categorification of a quantum cluster algebra, where $R$ is a symmetric KhovanovLaudaRouquier algebra. Roughly speaking, this criterion asserts that a quantum monoidal seed can be mutated successively in all the directions once the firststep mutations are possible. In the course of the study, we also give a proof of a conjecture of Leclerc on the product of upper global basis elements.
 Publication:

arXiv eprints
 Pub Date:
 December 2014
 DOI:
 10.48550/arXiv.1412.8106
 arXiv:
 arXiv:1412.8106
 Bibcode:
 2014arXiv1412.8106K
 Keywords:

 Mathematics  Representation Theory;
 Mathematics  Quantum Algebra;
 13F60;
 81R50;
 16G;
 17B37
 EPrint:
 44 pages