The critical CoHA of a quiver with potential Journal Article

Author(s): Davison, Ben
Article Title: The critical CoHA of a quiver with potential
Affiliation IST Austria
Abstract: 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.
Journal Title: Quarterly Journal of Mathematics
Volume: 68
Issue 2
ISSN: 1464-3847
Publisher: Oxford University Press  
Date Published: 2017-06-01
Start Page: 635
End Page: 703
Sponsor: Deutsche Forschungsgemeinschaft [grant number SFB/TR 45], European Research Council [grant number 320594], National Science Foundation [grant number DMS-0636646]
DOI: 10.1093/qmath/haw053
Open access: yes (repository)