English

The critical CoHA of a quiver with potential

Algebraic Geometry 2016-10-31 v5 High Energy Physics - Theory Representation Theory

Abstract

Pursuing the similarity between the Kontsevich--Soibelman construction of the cohomological Hall algebra of BPS states and Lusztig's construction of canonical bases for quantum enveloping algebras, and the similarity between the inetgrality conjecture for motivic Donaldson--Thomas invariants and the PBW theorem for quantum enveloping algebras, we build a coproduct on the cohomological Hall algebra associated to a quiver with potential. We also prove a cohomological dimensional reduction theorem, further linking a special class of cohomological Hall algebras with Yangians, and explaining how to connect the study of character varieties with the study of cohomological Hall algebras.

Keywords

Cite

@article{arxiv.1311.7172,
  title  = {The critical CoHA of a quiver with potential},
  author = {Ben Davison},
  journal= {arXiv preprint arXiv:1311.7172},
  year   = {2016}
}

Comments

Further minor corrections + Paper is largely rewritten, the notion of self-duality is dropped, hence the title change. Many thanks are due to the referees for a number of corrections regarding the content that survives from the previous version