Structure theorems of H4-Azumaya algebras

Let k be a field and H4 be Sweedlerʹs 4-dimensional algebra over k. It is well known that H4 has a family of triangular structures Rt indexed by the ground field k and each triangular structure Rt makes the H4-module category a braided monoidal category, denoted . In this paper, we study the Azumaya algebras in the categories . We obtain the structure theorems for Azumaya algebras in each braided monoidal category , t k. Utilizing the structure theorems we obtain a scalar invariant for each Azumaya algebra in the aforementioned categories.