Monoidal categorifications of cluster algebras of type A and D
Quantum Algebra
2013-03-07 v1 Rings and Algebras
Representation Theory
Abstract
In this note, we introduce monoidal subcategories of the tensor category of finite-dimensional representations of a simply-laced quantum affine algebra, parametrized by arbitrary Dynkin quivers. For linearly oriented quivers of types A and D, we show that these categories provide monoidal categorifications of cluster algebras of the same type. The proof is purely representation-theoretical, in the spirit of [arXiv:0903.1452].
Keywords
Cite
@article{arxiv.1207.3401,
title = {Monoidal categorifications of cluster algebras of type A and D},
author = {David Hernandez and Bernard Leclerc},
journal= {arXiv preprint arXiv:1207.3401},
year = {2013}
}
Comments
15 pages ; to appear in the proceedings of the Conference Symmetries, Integrable systems and Representations