Purely infinite simple Leavitt path algebras

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