Quantum dilogarithm identities for n-cycle quivers
Representation Theory
2018-12-04 v1
Abstract
We prove quantum dilogarithm identities for -cycle quivers. By the combinatorial approach of Keller, each side of our identity determines a maximal green sequence of quiver mutations. Thus we interpret our identities as factorizations of the refined Donaldson--Thomas invariant for the quiver with potential. Finally, we conjecture an upper bound on the possible lengths of maximal green sequences.
Cite
@article{arxiv.1812.00871,
title = {Quantum dilogarithm identities for n-cycle quivers},
author = {Justin Allman},
journal= {arXiv preprint arXiv:1812.00871},
year = {2018}
}
Comments
extended abstract submitted to FPSAC 2019; this version: 11 pages