Derivations of Leavitt path algebra

Abstract

In this paper, we describe the $K$-module $H{H}^1(L_K(\Gamma ))$ 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 give an explicit formula for every outer derivation of $L_K(\Gamma )$. We also describe the Lie algebra structure of outer derivations of the Toeplitz algebra and we prove that every derivation of the Leavitt path algebra can be extended to a derivation of the corresponding $C^{\ast }$-algebra.

References in corpus (5)

• Gröbner-Shirshov bases and their calculation
• Tensor products of Leavitt path algebras
• The Leavitt path algebra of a graph
• C*-algebras of separated graphs
• Homology of a Leavitt Path Algebra via Anick's Resolution