Derivations of Leavitt path algebras

In this paper, we describe the K-module HH1(L-K(Gamma)) of outer derivations of the Leavitt path algebra L-K(Gamma) of a row-finite graph Gamma with coefficients in an associative commutative ring K with unit. We explicitly describe a set of generators of HH1(L-K(Gamma)) and relations among them. We also describe a Lie algebra structure of outer derivation algebra of the Toeplitz algebra. We prove that every derivation of a Leavitt path algebra can be extended to a derivation of the corresponding C*-algebra. (C) 2018 Elsevier Inc. All rights reserved.