Endomorphism rings of Leavitt path algebras

We investigate conditions under which the endomorphism ring of the Leavitt path algebra $L_K(E)$ possesses various ring and module-theoretical properties such as being von Neumann regular, $\pi$-regular, strongly $\pi$-regular or self-injective. We also describe conditions under which $L_K(E)$ is continuous as well as automorphism invariant as a right $L_K(E)$-module.