Cohomological Hall algebra, exponential Hodge structures and motivic Donaldson–Thomas invariants

Abstract

To a quiver with potential we assign an algebra in the category of exponential mixed Hodge structures (the latter is also introduced in the paper). We compute the algebra (which we call Cohomological Hall algebra) for quivers without potential and study factorization properties of its Poincar-Hilbert series in general case. As an application we obtain an alternative approach to our theory of motivic Donaldson-Thomas invariants of 3-dimensional Calabi-Yau categories and prove their integrality properties. We discuss the relationship of Cohomological Hall algebra with other mathematical structures including cluster algebras and Chern-Simons theory.