Remarks on Cohomological Hall algebras and their representations

Abstract

The paper is devoted to several questions related to the notion of Cohomological Hall algebra (COHA for short) introduced few years ago by Maxim Kontsevich and the author. In particular we discuss a class of representations of COHA in the cohomology groups of the moduli spaces of stable framed objects. We speculate about possible sources of interesting representations as well as about some applications to geometry and physics.

Extended version of the talk at the workshop on Donaldson-Thomas invariants (Paris, June 2013)