Lifting graph $C^{\ast }$-algebra maps to Leavitt path algebra maps

Guillermo Cortiñas

Let $\xi :C^{\ast }(E)\to C^{\ast }(F)$ be a unital $\ast$-homomorphism between simple purely infinite Cuntz-Krieger algebras of finite graphs. We prove that there exists a unital $\ast$-homomorphism $…