Kavli Affiliate: Yukinobu Toda
| First 5 Authors: Yukinobu Toda, , , ,
| Summary:
We show that the categorified cohomological Hall algebra structures on
surfaces constructed by Porta-Sala descend to those on Donaldson-Thomas
categories on local surfaces introduced in the author’s previous paper. A
similar argument also shows that Pandharipande-Thomas categories on local
surfaces admit actions of categorified COHA for zero dimensional sheaves on
surfaces. We also construct annihilator actions of its simple operators, and
show that their commutator in the K-theory satisfies the relation similar to
the one of Weyl algebras. This result may be regarded as a categorification of
Weyl algebra action on homologies of Hilbert schemes of points on locally
planar curves due to Rennemo, which is relevant for Gopakumar-Vafa formula of
generating series of PT invariants.
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