Lp-OPERATOR ALGEBRAS ASSOCIATED WITH ORIENTED GRAPHS

For each 1 <= p <= infinity and each countable oriented graph Q we introduce an L-p-operator algebra O-p (Q), which contains the Leavitt path C-algebra L-Q as a dense subalgebra, and is universal for those L-p-representations of L-Q which are spatial in the sense of N.C. Phillips. We prove that O-p (Q) is simple as an L-p-operator algebra if and only if L-Q is simple, in which case it is isometrically isomorphic to <(rho(L-Q))over bar> for any nonzero spatial L-p-representation rho : L-Q -> L (L-p (X)). If moreover L-Q is purely infinite simple and p not equal p' then there is no nonzero continuous homomorphism O-p (Q) -> O-p' (Q).