Purely infinite simple Leavitt path algebras

We give necessary and sufficient conditions on a row-finite graph EE so that the Leavitt path algebra L(E)L(E) is purely infinite simple. This result provides the algebraic analog to the corresponding result for the Cuntz–Krieger C∗C∗-algebra C∗(E)C∗(E) given in [T. Bates, D. Pask, I. Raeburn, W. Szymański, The C∗C∗-algebras of row-finite graphs, New York J. Math. 6 (2000) 307–324].