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

Jiang Lining

doi:10.1090/S0002-9939-10-10315-3

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

Jiang Lining^*

^*此作品的通讯作者

数学学院

科研成果: 期刊稿件 › 文章 › 同行评审

3 引用（Scopus）

摘要

Suppose that G is a finite group and D(G) the quantum double algebra of G. Let A be the field algebra of G-spin models. There is a natural action of D(G) on A such that 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.

源语言	英语
页（从-至）	2793-2801
页数	9
期刊	Proceedings of the American Mathematical Society
卷	138
期	8
DOI	https://doi.org/10.1090/S0002-9939-10-10315-3
出版状态	已出版 - 8月 2010

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Lining, J. (2010). Towards a quantum galois theory for quantum double algebras of finite groups. Proceedings of the American Mathematical Society, 138(8), 2793-2801. https://doi.org/10.1090/S0002-9939-10-10315-3

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keywords = "Field algebra, G-spin models, Galois closed, Hopf algebra, Quantum double",

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AB - Suppose that G is a finite group and D(G) the quantum double algebra of G. Let A be the field algebra of G-spin models. There is a natural action of D(G) on A such that 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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KW - G-spin models

KW - Galois closed

KW - Hopf algebra

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

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