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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Towards a quantum Galois theory for quantum double algebras of finite groups


Author: Jiang Lining
Journal: Proc. Amer. Math. Soc. 138 (2010), 2793-2801
MSC (2010): Primary 46N50, 16T05
Published electronically: March 17, 2010
MathSciNet review: 2644893
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Abstract: Suppose that $ G$ is a finite group and $ D(G)$ the quantum double algebra of $ G$. Let $ \mathcal A$ be the field algebra of $ G$-spin models. There is a natural action of $ D(G)$ on $ \mathcal A$ such that $ \mathcal A$ becomes a $ D(G)$-module algebra. For a subgroup $ H$ of $ G$, there is a Hopf subalgebra $ D(G;H)$ of $ D(G)$. Based on the concrete construction of a $ D(G;H)$ fixed point subalgebra, the paper proves that $ D(G;H)$ is Galois closed and thus gives a quantum Galois theory in the field algebra of $ G$-spin models.


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Additional Information

Jiang Lining
Affiliation: Department of Mathematics, Beijing Institute of Technology, Beijing 100081, People’s Republic of China
Email: jianglining@bit.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-10-10315-3
PII: S 0002-9939(10)10315-3
Keywords: $G$-spin models, quantum double, field algebra, Hopf algebra, Galois closed.
Received by editor(s): January 19, 2009
Received by editor(s) in revised form: October 28, 2009
Published electronically: March 17, 2010
Additional Notes: This research is supported by the Program for New Century Excellent Talents in the University of China and by the National Science Foundation of China (10971011).
Communicated by: Marius Junge
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.