Purely infinite simple Leavitt path algebras
  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 [7]. 
G. Abrams, G. Aranda Pino