The critical CoHA of a quiver with potential
Abstract
Pursuing the similarity between the KontsevichSoibelman 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 DonaldsonThomas 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.
 Publication:

arXiv eprints
 Pub Date:
 November 2013
 arXiv:
 arXiv:1311.7172
 Bibcode:
 2013arXiv1311.7172D
 Keywords:

 Mathematics  Algebraic Geometry;
 High Energy Physics  Theory;
 Mathematics  Representation Theory
 EPrint:
 Further minor corrections + Paper is largely rewritten, the notion of selfduality 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