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Bibliographic Details
Main Author: Ohara, Mariko
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2401.05687
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author Ohara, Mariko
author_facet Ohara, Mariko
contents Let H be a finite dimensional Hopf algebra over a field k and A an H-module algebra over k. Khovanov and Qi defined acyclic objects and quasi-isomorphisms by using null-homotopy and contractible objects. They also defined the cofibrant objects, the derived category of A#H-modules, and showed properties of compact generators. On the other hand, a model structure on the category of A#H-modules are not mentioned yet. In this paper, we check that the category of A#H-modules admits a model structure, where the cofibrant objects and the derived category are just those defined by Qi. We also show that the model structure is cofibrantly generated.
format Preprint
id arxiv_https___arxiv_org_abs_2401_05687
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle A model structure on the category of equivariant A-modules over a Hopf algebra
Ohara, Mariko
K-Theory and Homology
16T05, 16S40, 18G65, 18G80, 20G42
Let H be a finite dimensional Hopf algebra over a field k and A an H-module algebra over k. Khovanov and Qi defined acyclic objects and quasi-isomorphisms by using null-homotopy and contractible objects. They also defined the cofibrant objects, the derived category of A#H-modules, and showed properties of compact generators. On the other hand, a model structure on the category of A#H-modules are not mentioned yet. In this paper, we check that the category of A#H-modules admits a model structure, where the cofibrant objects and the derived category are just those defined by Qi. We also show that the model structure is cofibrantly generated.
title A model structure on the category of equivariant A-modules over a Hopf algebra
topic K-Theory and Homology
16T05, 16S40, 18G65, 18G80, 20G42
url https://arxiv.org/abs/2401.05687