Derivations of Leavitt path algebras.

Abstract In this paper, we describe the K -module H H 1 (L K (Γ)) of outer derivations of the Leavitt path algebra L K (Γ) of a row-finite graph Γ with coefficients in an associative commutative ring K with unit. We explicitly describe a set of generators of H H 1 (L K (Γ)) 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. [ABSTRACT FROM AUTHOR]