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arXiv · 1509.05075

Derivations of Leavitt path algebra

Viktor Lopatkin
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Abstract

In this paper, we describe the $K$-module $HH^1(L_K(\Gamma))$ 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 $C^*$-algebra.

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BibTeXRIS

Viktor Lopatkin. 2015-09-16. Derivations of Leavitt path algebra. https://doi.org/10.1016/j.jalgebra.2018.11.011

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