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

Abstract

We define a new type of Hall algebras associated e.g. with quivers with polynomial potentials. The main difference with the conventional definition is that we use cohomology of the stack of representations instead of constructible sheaves or functions. In order to take into account the potential we introduce a generalization of theory of mixed Hodge structures, related to exponential integrals. Generating series of our Cohomological Hall algebra is a generalization of the motivic Donaldson-Thomas invariants introduced in arXiv:0811.2435. Also we prove a new integrality property of motivic Donaldson-Thomas invariants.

119 pages, corrected version

References in corpus (5)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Poisson automorphisms and quiver moduli
• Mutations for quivers with potentials: Oberwolfach talk, April 2007
• A DG guide to Voevodsky's motives
• On the de Rham Cohomology of Differential and Algebraic Stacks

Cited by in corpus (8)

• Motivic Donaldson-Thomas invariants and McKay correspondence
• On the Cohomological Hall Algebra of Dynkin quivers
• Borcherds Algebras and N=4 Topological Amplitudes
• Motivic Donaldson-Thomas invariants of the conifold and the refined topological vertex
• Nekrasov's Partition Function and Refined Donaldson-Thomas Theory: the Rank One Case
• Wall-crossing formulas for framed objects
• On the motivic Donaldson-Thomas invariants of quivers with potentials
• Kac's conjecture and the algebra of BPS states