# Symmetric structure of field algebra of G-spin models determined by a normal subgroup

## Abstract

Let G be a finite group and H a normal subgroup. D(H; G) is the crossed product of C(H) and CG which is only a subalgebra of D(G), the double algebra of G. One can construct a C*-subalgebra F{sub H} of the field algebra F of G-spin models, so that F{sub H} is a D(H; G)-module algebra, whereas F is not. Then the observable algebra A{sub (H,G)} is obtained as the D(H; G)-invariant subalgebra of F{sub H}, and there exists a unique C*-representation of D(H; G) such that D(H; G) and A{sub (H,G)} are commutants with each other.

- Authors:

- School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081 (China)

- Publication Date:

- OSTI Identifier:
- 22305869

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Mathematical Physics

- Additional Journal Information:
- Journal Volume: 55; Journal Issue: 9; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0022-2488

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; FIELD ALGEBRA; MATHEMATICAL MODELS; SPIN; SYMMETRY

### Citation Formats

```
Xin, Qiaoling, E-mail: xinqiaoling0923@163.com, and Jiang, Lining, E-mail: jianglining@bit.edu.cn.
```*Symmetric structure of field algebra of G-spin models determined by a normal subgroup*. United States: N. p., 2014.
Web. doi:10.1063/1.4896327.

```
Xin, Qiaoling, E-mail: xinqiaoling0923@163.com, & Jiang, Lining, E-mail: jianglining@bit.edu.cn.
```*Symmetric structure of field algebra of G-spin models determined by a normal subgroup*. United States. doi:10.1063/1.4896327.

```
Xin, Qiaoling, E-mail: xinqiaoling0923@163.com, and Jiang, Lining, E-mail: jianglining@bit.edu.cn. Mon .
"Symmetric structure of field algebra of G-spin models determined by a normal subgroup". United States. doi:10.1063/1.4896327.
```

```
@article{osti_22305869,
```

title = {Symmetric structure of field algebra of G-spin models determined by a normal subgroup},

author = {Xin, Qiaoling, E-mail: xinqiaoling0923@163.com and Jiang, Lining, E-mail: jianglining@bit.edu.cn},

abstractNote = {Let G be a finite group and H a normal subgroup. D(H; G) is the crossed product of C(H) and CG which is only a subalgebra of D(G), the double algebra of G. One can construct a C*-subalgebra F{sub H} of the field algebra F of G-spin models, so that F{sub H} is a D(H; G)-module algebra, whereas F is not. Then the observable algebra A{sub (H,G)} is obtained as the D(H; G)-invariant subalgebra of F{sub H}, and there exists a unique C*-representation of D(H; G) such that D(H; G) and A{sub (H,G)} are commutants with each other.},

doi = {10.1063/1.4896327},

journal = {Journal of Mathematical Physics},

issn = {0022-2488},

number = 9,

volume = 55,

place = {United States},

year = {2014},

month = {9}

}

DOI: 10.1063/1.4896327

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