Structure theorems of E(n)-Azumaya algebras

Abstract

Let k be a field and E(n) be the 2n+1-dimensional pointed Hopf algebra over k constructed by Beattie, Dăscălescu and Grunenfelder [J. Algebra, 2000, 225: 743–770]. E(n) is a triangular Hopf algebra with a family of triangular structures RM parameterized by symmetric matrices M in Mn(k). In this paper, we study the Azumaya algebras in the braided monoidal category \( E_{(n)} \mathcal{M}^{R_M } \) and obtain the structure theorems for Azumaya algebras in the category \( E_{(n)} \mathcal{M}^{R_M } \), where M is any symmetric n×n matrix over k.