The Field Algebra in Hopf Spin Models Determined by a Hopf *-Subalgebra and Its Symmetric Structure

Wei, Xiaomin; Jiang, Lining; Xin, Qiaoling

doi:10.1007/s10473-021-0317-8

Cited by 3 publications

(2 citation statements)

References 19 publications

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“…One can prove there is not the adjoint action of

ℂ H

on C ( G ), and then D ( H ; G ) can not be defined. Different from the case of D ( G ; H ), which is the crossed product of C ( G ) and

ℂ H

with respect to the adjoint action of the latter on the former, 9,13 D ( H ; G ) is not a Hopf subalgebra of D ( G ), even though it is a subalgebra of D ( G ). As to nonbalanced quantum double, one can refer to previous works 14,15 Also, the relation

S^{2} = id

holds in D ( H ; G ), which implies that ∀ a ∈ D ( H ; G ),

\begin{matrix} \begin{matrix} center \\ array \sum_{(a)} S (a_{(2)}) a_{(1)} = \sum_{(a)} a_{(2)} S (a_{(1)}) = ε (a) 1_{D (H; G)} . \end{matrix} \end{matrix}

…”

Section: The Structure Of the Observable Algebra In Scriptfhmentioning

confidence: 98%

“…Different from the case of D ( G ; H ), which is the crossed product of C ( G ) and

ℂ H

Section: The Structure Of the Observable Algebra In Scriptfhmentioning

confidence: 99%

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C^∗‐index of observable algebra in the field algebra determined by a normal group

Xin

Cao

Jiang

2021

Math Methods in App Sciences

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Let G be a finite group and H a normal subgroup. By D(H; G), we denote the crossed product of C(H) and CG, which is only a subalgebra of the quantum double D(G) of G. One can construct a C * -subalgebra  H of the field algebra  of G-spin models, such that  H is a D(H; G)-module algebra. The concrete construction of D(H; G)-invariant subalgebra  (H,G) of  H is given. Moreover, the C * -index of the conditional expectation z H from  H onto  (H,G) is calculated in terms of the quasi-basis for z H .

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“…One can prove there is not the adjoint action of

ℂ H

on C ( G ), and then D ( H ; G ) can not be defined. Different from the case of D ( G ; H ), which is the crossed product of C ( G ) and

ℂ H

S^{2} = id

holds in D ( H ; G ), which implies that ∀ a ∈ D ( H ; G ),

\begin{matrix} \begin{matrix} center \\ array \sum_{(a)} S (a_{(2)}) a_{(1)} = \sum_{(a)} a_{(2)} S (a_{(1)}) = ε (a) 1_{D (H; G)} . \end{matrix} \end{matrix}

…”

Section: The Structure Of the Observable Algebra In Scriptfhmentioning

confidence: 98%

“…Different from the case of D ( G ; H ), which is the crossed product of C ( G ) and

ℂ H

Section: The Structure Of the Observable Algebra In Scriptfhmentioning

confidence: 99%

C^∗‐index of observable algebra in the field algebra determined by a normal group

Xin

Cao

Jiang

2021

Math Methods in App Sciences

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Jones type C*-basic construction in non-equilibrium Hopf spin models

Wei,

Jiang

2023

Acta Math Sci

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The $$\hbox {C}^*$$-algebra index for observable algebra in non-equilibrium Hopf spin models

Wei

Jiang

2022

Ann. Funct. Anal.

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The Field Algebra in Hopf Spin Models Determined by a Hopf *-Subalgebra and Its Symmetric Structure

Cited by 3 publications

References 19 publications

C^∗‐index of observable algebra in the field algebra determined by a normal group

C^∗‐index of observable algebra in the field algebra determined by a normal group

Jones type C*-basic construction in non-equilibrium Hopf spin models

The $$\hbox {C}^*$$-algebra index for observable algebra in non-equilibrium Hopf spin models

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The Field Algebra in Hopf Spin Models Determined by a Hopf *-Subalgebra and Its Symmetric Structure

Cited by 3 publications

References 19 publications

C∗‐index of observable algebra in the field algebra determined by a normal group

C∗‐index of observable algebra in the field algebra determined by a normal group

Jones type C*-basic construction in non-equilibrium Hopf spin models

The $$\hbox {C}^*$$-algebra index for observable algebra in non-equilibrium Hopf spin models

Contact Info

Product

Resources

About

C^∗‐index of observable algebra in the field algebra determined by a normal group

C^∗‐index of observable algebra in the field algebra determined by a normal group