Remarks on Cohomological Hall algebras and their representations

TL;DR

This paper explores the structure and representations of Cohomological Hall algebras (COHA), discussing their potential applications in geometry and physics, and proposing new directions for understanding their role in mathematical physics.

Contribution

It introduces a class of COHA representations in the cohomology of moduli spaces and discusses their potential sources and applications, advancing the understanding of COHA's role in geometry and physics.

Findings

Identified a new class of COHA representations in moduli space cohomology

Proposed potential sources for interesting COHA representations

Discussed applications of COHA in geometry and physics

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.