Structure theorems of <Emphasis Type="Italic">E</Emphasis>(<Emphasis Type="Italic">n</Emphasis>)-Azumaya algebras |
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Authors: | Ying Zhang Huixiang Chen Haibo Hong |
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Institution: | 1.School of Mathematics Science,Yangzhou University,Yangzhou,China |
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Abstract: | Let k be a field and E(n) be the 2
n+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_{(n)} \mathcal{M}^{R_M }
$
E_{(n)} \mathcal{M}^{R_M }
and obtain the structure theorems for Azumaya algebras in the category $
E_{(n)} \mathcal{M}^{R_M }
$
E_{(n)} \mathcal{M}^{R_M }
, where M is any symmetric n×n matrix over k. |
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Keywords: | |
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