Structure theorems of E(n)-Azumaya algebras

Abstract

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