The generic Markov CoHA is not spherically generated
Year: 2025
Type: article
Abstract: Let $Q$ be the Markov quiver, and let $W$ be an infinitely mutable potential for $Q$. We calculate some low degree refined BPS invariants for the resulting Jacobi algebra, and use them to show that the critical cohomological Hall algebra $\mathcal{H}_{Q,W}$ is not necessarily spherically generated, and is not independent of the choice of infinitely mutable potential $W$. This leads to a counterexample to a conjecture of Gaiotto, Grygoryev and Li \cite[§2.1]{GGL}, but also suggestions for how to modify it. In the case of generic cubic $W$, we discuss a way to modify the conjecture, by excluding the non-spherical part via the decomposition of $\mathcal{H}_{Q,W}$ according to the characters of a discrete symmetry group.
Author: Davison, Ben
Institution: Maxwell Institute for Mathematical Sciences
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4407310219