A quantum cluster algebra structure on the semi-derived Hall algebra
Representation Theory
2024-10-25 v1
Abstract
Using Hernandez-Leclerc's isomorphism between the derived Hall algebra of a representation-finite quiver and the quantum Grothendieck ring of the quantum loop algebra of the Dynkin type of , we lift the (quantum) cluster algebra structure of the quantum Grothendieck ring to the semi-derived Hall algebra, introduced by Gorsky, of the category of bounded complexes of projective modules over the path algebra of . We also construct a braid group action on the semi-derived Hall algebra, lifting Kashiwara-Kim-Oh-Park's braid group action on the quantum Grothendieck ring.
Keywords
Cite
@article{arxiv.2410.18604,
title = {A quantum cluster algebra structure on the semi-derived Hall algebra},
author = {Alessandro Contu},
journal= {arXiv preprint arXiv:2410.18604},
year = {2024}
}