Comparison of Cohomological and K-theoretical Hall algebra

TL;DR

This paper constructs a conceptual comparison between K-theoretical and cohomological Hall algebras for symmetric quivers and extends the comparison to quivers with potential.

Contribution

It provides a new, more conceptual construction of the algebra morphism and extends the comparison to quivers with potential.

Findings

Established a comparison algebra morphism for symmetric quivers.

Extended the comparison to quivers with potential.

Provided a more conceptual framework for the algebraic relationship.

Abstract

We give a more conceptual construction of a comparison algebra morphism from the K-theoretical Hall algebra to a twist of the cohomological Hall algebra associated to a symmetric quiver, and extend the result to quivers with potential.