Homotopy quotients and comodules of supercommutative Hopf algebras
| Autor: | Heidersdorf, Thorsten, Weissauer, Rainer |
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| Rok vydání: | 2019 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We study induced model structures on Frobenius categories. In particular we consider the case where $\mathcal{C}$ is the category of comodules of a supercommutative Hopf algebra $A$ over a field $k$. Given a graded Hopf algebra quotient $A \to B$ satisfying some finiteness conditions, the Frobenius tensor category $\mathcal{D}$ of graded $B$-comodules with its stable model structure induces a monoidal model structure on $\mathcal{C}$. We consider the corresponding homotopy quotient $\gamma: \mathcal{C} \to Ho \mathcal{C}$ and the induced quotient $\mathcal{T} \to Ho \mathcal{T}$ for the tensor category $\mathcal{T}$ of finite dimensional $A$-comodules. Under some mild conditions we prove vanishing and finiteness theorems for morphisms in $Ho \mathcal{T}$. We apply these results in the $Rep (GL(m|n))$-case and study its homotopy category $Ho \mathcal{T}$. Comment: v3: Minor changes, added lemma 6.2, assumed char 0 even in part 1. v2: Removed a few typos. v1: 77 pages |
| Databáze: | arXiv |
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