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arXiv · 0906.4376

The socle series of a Leavitt path algebra

Gene Abrams·Kulumani M. Rangaswamy·Mercedes Siles Molina
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Abstract

We investigate the ascending Loewy socle series of Leavitt path algebras $L_K(E)$ for an arbitrary graph $E$ and field $K$. We classify those graphs $E$ for which $L_K(E)=S_λ$ for some element $S_λ$ of the Loewy socle series. We then show that for any ordinal $λ$ there exists a graph $E$ so that the Loewy length of $L_K(E)$ is $λ$. Moreover, $λ\leq ω$ (the first infinite ordinal) if $E$ is a row-finite graph.

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Gene Abrams, Kulumani M. Rangaswamy, Mercedes Siles Molina. 2009-06-23. The socle series of a Leavitt path algebra. https://arxiv.org/abs/0906.4376

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