---
_id: '687'
abstract:
- lang: eng
  text: Pursuing the similarity between the Kontsevich-Soibelman construction of the
    cohomological Hall algebra (CoHA) of BPS states and Lusztig's construction of
    canonical bases for quantum enveloping algebras, and the similarity between the
    integrality conjecture for motivic Donaldson-Thomas invariants and the PBW theorem
    for quantum enveloping algebras, we build a coproduct on the CoHA associated to
    a quiver with potential. We also prove a cohomological dimensional reduction theorem,
    further linking a special class of CoHAs with Yangians, and explaining how to
    connect the study of character varieties with the study of CoHAs.
article_processing_charge: No
arxiv: 1
author:
- first_name: Ben
  full_name: Davison, Ben
  id: 4634AB1E-F248-11E8-B48F-1D18A9856A87
  last_name: Davison
  orcid: 0000-0002-8944-4390
citation:
  ama: Davison B. The critical CoHA of a quiver with potential. <i>Quarterly Journal
    of Mathematics</i>. 2017;68(2):635-703. doi:<a href="https://doi.org/10.1093/qmath/haw053">10.1093/qmath/haw053</a>
  apa: Davison, B. (2017). The critical CoHA of a quiver with potential. <i>Quarterly
    Journal of Mathematics</i>. Oxford University Press. <a href="https://doi.org/10.1093/qmath/haw053">https://doi.org/10.1093/qmath/haw053</a>
  chicago: Davison, Ben. “The Critical CoHA of a Quiver with Potential.” <i>Quarterly
    Journal of Mathematics</i>. Oxford University Press, 2017. <a href="https://doi.org/10.1093/qmath/haw053">https://doi.org/10.1093/qmath/haw053</a>.
  ieee: B. Davison, “The critical CoHA of a quiver with potential,” <i>Quarterly Journal
    of Mathematics</i>, vol. 68, no. 2. Oxford University Press, pp. 635–703, 2017.
  ista: Davison B. 2017. The critical CoHA of a quiver with potential. Quarterly Journal
    of Mathematics. 68(2), 635–703.
  mla: Davison, Ben. “The Critical CoHA of a Quiver with Potential.” <i>Quarterly
    Journal of Mathematics</i>, vol. 68, no. 2, Oxford University Press, 2017, pp.
    635–703, doi:<a href="https://doi.org/10.1093/qmath/haw053">10.1093/qmath/haw053</a>.
  short: B. Davison, Quarterly Journal of Mathematics 68 (2017) 635–703.
corr_author: '1'
date_created: 2018-12-11T11:47:55Z
date_published: 2017-06-01T00:00:00Z
date_updated: 2025-09-10T14:15:30Z
day: '01'
department:
- _id: TaHa
doi: 10.1093/qmath/haw053
ec_funded: 1
external_id:
  arxiv:
  - '1311.7172'
  isi:
  - '000404545300015'
intvolume: '        68'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1311.7172
month: '06'
oa: 1
oa_version: Submitted Version
page: 635 - 703
project:
- _id: 25E549F4-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '320593'
  name: Arithmetic and physics of Higgs moduli spaces
publication: Quarterly Journal of Mathematics
publication_identifier:
  issn:
  - 0033-5606
publication_status: published
publisher: Oxford University Press
publist_id: '7022'
quality_controlled: '1'
scopus_import: '1'
status: public
title: The critical CoHA of a quiver with potential
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 68
year: '2017'
...