11 papers
Commutativity of nilpotent cohomological Hall algebras of
Lucien Hennecart
In this paper, we prove that both the seminilpotent and the fully nilpotent CoHAs of are commutative. This result is in strong contrast with the CoHA of $\mathbf{A}^…
Hecke operators on symplectic surfaces and -independence
Ben Davison, Lucien Hennecart, Tasuki Kinjo +2
We prove Toda's chi-independence conjecture for the BPS cohomology of moduli spaces of one-dimensional sheaves on quasi-projective symplectic surfaces, relative to the Chow variety…
The Deligne-Simpson problem via 2-Calabi-Yau categories
Lucien Hennecart
We provide a short proof of the necessity of Crawley-Boevey's condition in his solution to the Deligne-Simpson problem. The proof relies on the local neighbourhood theorem for -…
Degenerations of CoHAs of 2-Calabi-Yau categories
Lucien Hennecart, Shivang Jindal
By work of Davison and Meinhardt, the cohomological Hall algebra of a symmetric quiver with potential admits a geometrically defined filtration (the perverse filtration) whose asso…
The BPS decomposition theorem
Lucien Hennecart, Tasuki Kinjo
We prove the BPS decomposition theorem (a.k.a. cohomological integrality theorem) decomposing the cohomology of smooth symmetric stacks into the Weyl-invariant part of the cohomolo…
BPS algebras and generalised Kac-Moody algebras from 2-Calabi-Yau categories
Ben Davison, Lucien Hennecart, Sebastian Schlegel Mejia
We determine the structure of the BPS algebra of 2-Calabi-Yau Abelian categories for which the stack of objects admits a good moduli space. We prove that this algebra is isomorphic…