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.
- Pub Date:
- November 2013
- Mathematics - Algebraic Geometry;
- High Energy Physics - Theory;
- Mathematics - Representation Theory
- 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