Symmetric states for C∗-Fermi systems

In the present note, which is second part of a work concerning study set symmetric states, we introduce extension Klein transformation for general Fermi tensor product two $\bz^2$ graded $C^*$-algebras, under condition that grading one involved algebras inner. After extending construction to $C^*$-inductive limits, such realises canonical $*$-isomorphism between $\bz^2$-graded $C^*$-algebras made infinite $C^*$-tensor and single $C^*$-algebra, both built with respect corresponding minimal $C^*$-cross norms. It preserves grading, its transpose sends even states $\ga_{\rm X}$ in (necessarily even) on F}$, therefore induces an isomorphism simplexes $$ \cs_\bp(\ga_{\rm F})=\cs_{\bp\times\bz^2}(\ga_{\rm F})\sim\cs_{\bp\times\bz^2}(\ga_{\rm X})\,, allows reduce structure $C^*$-Fermi systems usual product. Other relevant properties algebra will be proved without use transformation. We end example not implementable, simply because does generate Therefore, general, cannot reduced product, if share many common properties.