Affine group dg-schemes and linear representations I - Basic theory and\n Tannakian reconstructions

2019/04/05 by Jaehyeok Lee, Lee, Jaehyeok, Jae-Suk Park +1
Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.1904.03162

openalex publication_date 2019/04/05 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28

Abstract

We develop a basic theory of affine group dg-schemes, their Lie algebraic\ncounterparts and linear representations. We prove Tannaka type reconstruction\ntheorems that an affine group dg-scheme can be recovered from the dg-tensor\ncategory of its linear representations as well as from the rigid dg-tensor\ncategory of its finite dimensional linear representations along with the\nforgetful functors to the underlying dg-tensor category of cochain complexes.\n

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