Matches in SemOpenAlex for { <https://semopenalex.org/work/W4311726053> ?p ?o ?g. }
Showing items 1 to 57 of
57
with 100 items per page.
- W4311726053 abstract "We define and study a sheaf-theoretic cohomological Hall algebra for suitably geometric Abelian categories $mathcal{A}$ of homological dimension at most two, and a sheaf-theoretic BPS algebra under the conditions that $mathcal{A}$ is 2-Calabi-Yau and has a good moduli space. We show that the BPS algebra for the preprojective algebra $Pi_Q$ of a totally negative quiver is the free algebra generated by the intersection cohomology of the closure of the locus parameterising simple $Pi_Q$-modules in the coarse moduli space. We define and study the BPS Lie algebra of arbitrary 2-Calabi-Yau categories $mathcal{A}$ for which the Euler form is negative on all pairs of non-zero objects, which recovers the BPS algebra as its universal enveloping algebra for such totally negative 2CY categories. We show that for totally negative 2CY categories the BPS algebra is freely generated by intersection complexes of certain coarse moduli spaces as above, and the Borel-Moore homology of the stack of objects in such $mathcal{A}$ satisfies a Yangian-type PBW theorem for the BPS Lie algebra. In this way we prove the cohomological integrality theorem for these categories. We use our results to prove that for $C$ a smooth projective curve, and for $r$ and $d$ not necessarily coprime, there is a nonabelian Hodge isomorphism between the Borel-Moore homologies of the stack of rank $r$ and degree $d$ Higgs bundles, and the appropriate stack of twisted representations of the fundamental group of $C$. In addition we prove the Bozec-Schiffmann positivity conjecture for totally negative quivers; we prove that their polynomials counting cuspidal functions in the constructible Hall algebra for $Q$ have positive coefficients, strengthening the positivity theorem for the Kac polynomials of such quivers." @default.
- W4311726053 created "2022-12-28" @default.
- W4311726053 creator A5026513396 @default.
- W4311726053 creator A5041225859 @default.
- W4311726053 creator A5053149202 @default.
- W4311726053 date "2022-12-15" @default.
- W4311726053 modified "2023-10-16" @default.
- W4311726053 title "BPS Lie algebras for totally negative 2-Calabi-Yau categories and nonabelian Hodge theory for stacks" @default.
- W4311726053 doi "https://doi.org/10.48550/arxiv.2212.07668" @default.
- W4311726053 hasPublicationYear "2022" @default.
- W4311726053 type Work @default.
- W4311726053 citedByCount "0" @default.
- W4311726053 crossrefType "posted-content" @default.
- W4311726053 hasAuthorship W4311726053A5026513396 @default.
- W4311726053 hasAuthorship W4311726053A5041225859 @default.
- W4311726053 hasAuthorship W4311726053A5053149202 @default.
- W4311726053 hasBestOaLocation W43117260531 @default.
- W4311726053 hasConcept C136119220 @default.
- W4311726053 hasConcept C144091092 @default.
- W4311726053 hasConcept C155058155 @default.
- W4311726053 hasConcept C158260368 @default.
- W4311726053 hasConcept C202444582 @default.
- W4311726053 hasConcept C33923547 @default.
- W4311726053 hasConcept C4017995 @default.
- W4311726053 hasConcept C51568863 @default.
- W4311726053 hasConcept C67996461 @default.
- W4311726053 hasConcept C73373263 @default.
- W4311726053 hasConcept C78606066 @default.
- W4311726053 hasConcept C95857938 @default.
- W4311726053 hasConceptScore W4311726053C136119220 @default.
- W4311726053 hasConceptScore W4311726053C144091092 @default.
- W4311726053 hasConceptScore W4311726053C155058155 @default.
- W4311726053 hasConceptScore W4311726053C158260368 @default.
- W4311726053 hasConceptScore W4311726053C202444582 @default.
- W4311726053 hasConceptScore W4311726053C33923547 @default.
- W4311726053 hasConceptScore W4311726053C4017995 @default.
- W4311726053 hasConceptScore W4311726053C51568863 @default.
- W4311726053 hasConceptScore W4311726053C67996461 @default.
- W4311726053 hasConceptScore W4311726053C73373263 @default.
- W4311726053 hasConceptScore W4311726053C78606066 @default.
- W4311726053 hasConceptScore W4311726053C95857938 @default.
- W4311726053 hasLocation W43117260531 @default.
- W4311726053 hasOpenAccess W4311726053 @default.
- W4311726053 hasPrimaryLocation W43117260531 @default.
- W4311726053 hasRelatedWork W1650411932 @default.
- W4311726053 hasRelatedWork W1989503713 @default.
- W4311726053 hasRelatedWork W1998546512 @default.
- W4311726053 hasRelatedWork W2093169653 @default.
- W4311726053 hasRelatedWork W2122511132 @default.
- W4311726053 hasRelatedWork W2953154532 @default.
- W4311726053 hasRelatedWork W2982581780 @default.
- W4311726053 hasRelatedWork W3097108988 @default.
- W4311726053 hasRelatedWork W3112868807 @default.
- W4311726053 hasRelatedWork W4287116780 @default.
- W4311726053 isParatext "false" @default.
- W4311726053 isRetracted "false" @default.
- W4311726053 workType "article" @default.