Monotonic Property in Field Algebra of G—Spin Model

Let F be the field algebra of G-spin model,D(G)the double algebra of a finite group G and D(H)the sub-Hopf algerba of D(G)determined by the subgroup H of G.The paper builds a correspondence between D(H)and the D(H)-invariant sub-C*-algebra AH in F,and proves that the correspondence is strictly monotonic.     

Gelfand-Naimark Theorem of Commutative Hopf C^＊ -Algebras

LetGbeacompactgroupwithaunitee,and C(G)thespaceofallcomplexcontinuousfunctions onG.C(G)isaC algebrawithproductdefined by(fg)(t)=f(t)g(t)andthestandardinvolution definedbyf(t)=f(t)(f,g∈C(G),t∈G).Underthestructuremaps(Δf)(s,t)=f(st),ε(f)=f(e)and(Sf)(t)=f(t-1),C(G)be comesaHopfalgebra.IfGisalocallycompact group,letC0(G)bethespaceofcomplexcontinuous functionsonGtendingto0atinfinity,C0(G)isal soaC algebra.HoweverC0(G)hasnounit,this leadstotheconceptofamultiplierHopfalgebra[1].Aswehave…     

C^＊-Structure of Quantum Double for Finite Hopf C^＊-Algebra

Let H be a finite Hopf C^＊ -algebra and H′be its dual Hopf algebra. Drinfeld＇s quantum double D（H） of H is a Hopf^＊-algebra. There is a faithful positive linear functional θ on D（H）. Through the associated Gelfand-Naimark-Segal （GNS） representation, D（H） has a faithful^＊ -representation so that it becomes a Hopf C^＊ -algebra. The canonical embedding map of H into D（H） is isometric.