Structure theorems of [formula omitted]-Azumaya algebras

Abstract

Let k be a field and H 4 be Sweedler's 4-dimensional algebra over k. It is well known that H 4 has a family of triangular structures R t indexed by the ground field k and each triangular structure R t makes the H 4 -module category M H 4 a braided monoidal category, denoted M R t H 4 . In this paper, we study the Azumaya algebras in the categories M R t H 4 . We obtain the structure theorems for Azumaya algebras in each braided monoidal category M R t H 4 , t ∈ k . Utilizing the structure theorems we obtain a scalar invariant for each Azumaya algebra in the aforementioned categories.