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 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\left(n\right)}{ℳ}^{R_M} and obtain the structure theorems for Azumaya algebras in the category {}_{E\left(n\right)}{ℳ}^{R_M}, where M is any symmetric n × n matrix over k.

Keywords

Yetter-Drinfeld module / Brauer group / Azumaya algebra

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