E (n)-azumaya Algebra Structure

Let k be a field and E(n) be a Hopf algebra over k, where char k≠2, n be a positive integer. Sweedler's 4-dimentional Hopf algebra H₄ can be regarded as a subHopf algebra of E(n). E(n) has a triangular structure R₀ and R₀ makes the E(n)-module category _E(n)M a braided monoidal category, denoted _E(n)M^R₀. In this paper, we study the Azumaya algebras in the category _E(n)M^R₀. We obtain the structure theorems for Azumaya algebras in braided monoidal category _E(n)M^R₀. Utilizing the structure theorems we obtain symmetric matrix invariants for Azumaya algebras in the aforementioned category. Moreover, equivalent (E(n),R₀)-Azumaya algebras share the same symmetric matrix invariant.