Four-dimensional Yetter–Drinfeld module algebras over H4

Abstract In this paper, we classify four-dimensional Yetter–Drinfeld module algebras over Sweedler's 4-dimensional Hopf algebra H 4 . All H 4 -Azumaya algebras of dimension 4 have been given. In particular, all Yetter–Drinfeld H 4 -module algebra structures on the matrix algebra M 2 ( k ) are classified.