On the motivic Donaldson-Thomas invariants of quivers with potentials

We study motivic Donaldson-Thomas invariants for a class of quivers with potentials using the strategy of Behrend, Bryan, and Szendroi. This class includes quivers with potentials arising from consistent brane tilings and quivers with zero potential. Our construction is an alternative to the constructions of Kontsevich and Soibelman. We construct an integration map from the equivariant Hall algebra to the quantum torus and show that our motivic Donaldson-Thomas invariants are images of the natural elements in the equivariant Hall algebra. We show that the inegration map is an algebra homomorphism and use this fact to prove the Harder-Narasimhan relation for the motivic Donaldson-Thomas invariants.