Kavli Affiliate: Yukinobu Toda
| First 5 Authors: Tudor Pădurariu, Yukinobu Toda, , ,
| Summary:
We study certain categories associated to symmetric quivers with potential,
called quasi-BPS categories. We construct semiorthogonal decompositions of the
categories of matrix factorizations for moduli stacks of representations of
(framed or unframed) symmetric quivers with potential, where the summands are
categorical Hall products of quasi-BPS categories. These results generalize our
previous results about the three loop quiver.
We prove several properties of quasi-BPS categories: wall-crossing
equivalence, strong generation, and categorical support lemma in the case of
tripled quivers with potential. We also introduce reduced quasi-BPS categories
for preprojective algebras, which have trivial relative Serre functor and are
indecomposable when the weight is coprime with the total dimension. In this
case, we regard the reduced quasi-BPS categories as noncommutative local
hyperk"ahler varieties, and as (twisted) categorical versions of crepant
resolutions of singularities of good moduli spaces of representations of
preprojective algebras.
The studied categories include the local models of quasi-BPS categories of K3
surfaces. In a follow-up paper, we establish analogous properties for quasi-BPS
categories of K3 surfaces.
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