Structure theorems of H4-Azumaya algebras

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-H4 a braided monoidal category, denoted M-H4(Rt). In this paper, we study the Azumaya algebras in the categories (H4)M4(Rt). We obtain the structure theorems for Azumaya algebras in each braided monoidal category M-H4(Rt), t is an element of k. Utilizing the structure theorems we obtain a scalar invariant for each Azumaya algebra in the aforementioned categories. (c) 2005 Elsevier Inc. All rights reserved.