COMPLETELY POSITIVE MAPS AND $*$-OMORPHISM OF $\[{C^*}\]$-ALGEBRAS

Let $A$, $B$ be unital $\{C^*}\]$-algebras. $\{\chi _A} = \{ \varphi |\varphi \]$ are all completely postive linear maps from $\{M_n}(C)\]$ to $A$ with $\\left\| {a(\varphi )} \right\| \le 1\]$ $}$. $\(a(\varphi ) = \left( {\begin{array}{*{20}{c}} {\varphi ({e_{11}})}& \cdots &{\varphi ({e_{1n}})}\{}& \cdots &{}\{\varphi ({e_{n1}})}& \cdots &{\varphi ({e_{nn}})} \end{array}} \right),\]$ where $\\{ {e_{ij}}\} \]$ is the matrix unit of $\{M_n}(C)\]$. Let $\\alpha \]$ be the natural action of $\SU(n)\]$ on $\{M_n}(C)\]$ For $\n \ge 3\]$, if $\\Phi \]$ is an $\\alpha \]$-invariant affine isomorphism between $\{\chi _A}\]$ and $\{\chi _B}\]$, $\\Phi (0) = 0\]$, then $A$ and $B$ are $\^*\]$-isomorphic In this paper a counter example is given for the case $\n = 2\]$.