Four-dimensional Yetter–Drinfeld module algebras over H4

In this paper, we classify four-dimensional Yetter–Drinfeld module algebras over Sweedlerʹs 4-dimensional Hopf algebra H4. All H4-Azumaya algebras of dimension 4 have been given. In particular, all Yetter–Drinfeld H4-module algebra structures on the matrix algebra M2(k) are classified.