@article{Dong2023, 
author = {Jinlei Dong and Fang Li and Longgang Sun},
title = {Derived equivalence, recollements under    H-Galois extensions},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {2},
pages = {3210-3225},
keywords = {recollement, tilting complex, H-Galois extension, H-Frobenius extension},
url = {https://www.sciopen.com/article/10.3934/math.2023165},
doi = {10.3934/math.2023165},
abstract = {In this paper, assume that    H is a Hopf algebra and    A      /    B is an    H-Galois extension. Firstly, by introducing the concept of an    H-stable tilting complex        T          ∙       over    B, we show that        T          ∙            ⊗    B    A is a tilting complex over    A and a derived equivalence between two    H-module algebras can be extended to smash product algebras under some conditions. Then we observe that    0  →            E      n      d                                D                b            (      B      )        (      T          ∙        )  →            E      n      d                                D                b            (      A      )        (      T          ∙            ⊗    B    A  ) is an    H-Galois Frobenius extension if    A      /    B is an    H-Galois Frobenius extension. Finally, for any perfect recollement of derived categories of    H-module algebras, we apply the above results to construct a perfect recollement of derived categories of their smash product algebras and generalize it to    n-recollements.}
}