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Factorisation quantum groups

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arxiv 2312.07274 v1 pith:TNT4JE5Y submitted 2023-12-12 math.AG math.QA

Alexei Latyntsev This is my paper · ORCID
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keywords vertexalgebrafactorisationtheoryalgebrasanalogouslyanaloguesbialgebras
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We develop vertex and factorisation algebra analogues of the theory of quasitriangular bialgebras. Analogously to the classical theory, we prove their categories of representations are controlled by spectral R-matrices. In the vertex algebra case this generalises previous notions due to Etingof-Kazhdan and Frenkel-Reshetikhin. Finally we give examples, including Borcherds twists and homology vertex algebras.

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  1. Orthosymplectic modules of cohomological Hall algebras

    math.AG 2025-01 conditional novelty 7.0 of 10

    Classical type parabolic induction produces twisted Yetter-Drinfeld vertex modules for cohomological Hall algebras, including cases of dimension-zero sheaves on surfaces.

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