Simplicity of the Lie algebra of skew symmetric elements of a Leavitt path algebra

Adel Alahmedi; Hamed Alsulami

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arXiv · 1304.2385

Simplicity of the Lie algebra of skew symmetric elements of a Leavitt path algebra

Adel Alahmedi·Hamed Alsulami

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Abstract

For a field $F$ of characteristic not 2 and a directed row-finite graph $\Gamma$ let $L(\Gamma)$ be the Leavitt path algebra with the standard involution $*.$ We study the Lie algebra $K=K(L(\Gamma),*)$ of $*-$skew-symmetric elements and find necessary and sufficient conditions for the Lie algebra $[K,K]$ to be simple.

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Adel Alahmedi, Hamed Alsulami. 2013-04-06. Simplicity of the Lie algebra of skew symmetric elements of a Leavitt path algebra. https://arxiv.org/abs/1304.2385

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