English

Quantum dilogarithm identities for n-cycle quivers

Representation Theory 2018-12-04 v1

Abstract

We prove quantum dilogarithm identities for nn-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

R2 v1 2026-06-23T06:29:36.533Z