Frontiers of Mathematics in China >

2010 , Vol. 5 >Issue 4: 757 - 776

DOI: https://doi.org/10.1007/s11464-010-0066-9

RESEARCH ARTICLE

Structure theorems of E(n)-Azumaya algebras

  • Ying ZHANG ,
  • Huixiang CHEN ,
  • Haibo HONG
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  • School of Mathematics Science, Yangzhou University, Yangzhou 225002, China

Received date: 23 Feb 2010

Accepted date: 16 Apr 2010

Published date: 05 Dec 2010

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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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 RM parameterized by symmetric matrices M in Mn(k). In this paper, we study the Azumaya algebras in the braided monoidal category E(n)ℳRM and obtain the structure theorems for Azumaya algebras in the category E(n)ℳRM, where M is any symmetric n × n matrix over k.

Key words： Yetter-Drinfeld module; Brauer group; Azumaya algebra

Cite this article

Ying ZHANG , Huixiang CHEN , Haibo HONG . Structure theorems of E(n)-Azumaya algebras[J]. Frontiers of Mathematics in China, 2010 , 5(4) : 757 -776 . DOI: 10.1007/s11464-010-0066-9

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