2024/01/11 by Mariko Ohara, Ohara, Mariko
Mathematics · #16S40 #16T05 #18G65 #18G80 #20G42 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)
paper · pdf · doi:10.48550/arxiv.2401.05687
openalex publication_date 2024/01/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.