Homotopy quotients and comodules of supercommutative Hopf algebras

• Verfasst von: Heidersdorf, Thorsten [VerfasserIn]
• Verfasst von: Weissauer, Rainer [VerfasserIn]
• Titel: Homotopy quotients and comodules of supercommutative Hopf algebras
• Verf.angabe: Thorsten Heidersdorf, Rainer Weissauer
• E-Jahr: 2024
• Jahr: 12 August 2024
• Umfang: 73 S.
• Illustrationen: Illustrationen
• Fussnoten: Online veröffentlicht: 12. August 2024 ; Gesehen am 23.07.2025
• Titel Quelle: Enthalten in: Applied categorical structures
• Ort Quelle: Dordrecht [u.a.] : Springer Science + Business Media B.V, 1993
• Jahr Quelle: 2024
• Band/Heft Quelle: 32(2024), 5, Artikel-ID 23, Seite 1-73
• ISSN Quelle: 1572-9095
• DOI: doi:10.1007/s10485-024-09781-0
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: 16T15
• Sach-SW: 17B10
• Sach-SW: 18D10
• Sach-SW: 18E40
• Sach-SW: 18G55
• Sach-SW: 20G05
• Sach-SW: 55U35
• Sach-SW: Algebraic Geometry
• Sach-SW: Algebraic supergroups
• Sach-SW: Algebraic Topology
• Sach-SW: Associative Rings and Algebras
• Sach-SW: Category Theory, Homological Algebra
• Sach-SW: Commutative Rings and Algebras
• Sach-SW: General linear supergroup
• Sach-SW: Homotopy categories
• Sach-SW: Model categories
• Sach-SW: Non-associative Rings and Algebras
• Sach-SW: Supercommutative Hopf algebras
• K10plus-PPN: 1931580456

Abstract

We study model structures on the category of comodules of a supercommutative Hopf algebra A over fields of characteristic 0. Given a graded Hopf algebra quotient A → B satisfying some finiteness conditions, the Frobenius tensor category D of graded B-comodules with its stable model structure induces a monoidal model structure on C. We consider the corresponding homotopy quotient gamma : C → HoC and the induced quotient T → HoT for the tensor category T of finite dimensional A-comodules. Under some mild conditions we prove vanishing and finiteness theorems for morphisms in HoT. We apply these results in the Rep(GL(m|n))-case and study its homotopy category HoT associated to the parabolic subgroup of upper triangular block matrices. We construct cofibrant replacements and show that the quotient of HoT by the negligible morphisms is again the representation category of a supergroup scheme.