Automorphisms of Leavitt path algebras: Zhang twist and irreducible representations

Abstract

In this article, we construct (graded) automorphisms fixing all vertices of Leavitt path algebras of arbitrary graphs in terms of general linear groups over corners of these algebras. As an application, we study Zhang twist of Leavitt path algebras and describe new classes of irreducible representations of Leavitt path algebras of rose graphs Rn with n petals.