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arXiv · 2207.03419

Injectives over Leavitt path algebras of graphs with disjoint cycles

Gene Abrams·Francesca Mantese·Alberto Tonolo
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Abstract

Let $K$ be any field, and let $E$ be a finite graph with the property that every vertex in $E$ is the base of at most one cycle (we say such a graph satisfies Condition (AR)). We explicitly construct the injective envelope of each simple left module over the Leavitt path algebra $L_K(E)$. The main idea girding our construction is that of a "formal power series" extension of modules, thereby developing for all graphs satisfying Condition (AR) the understanding of injective envelopes of simple modules over $L_K(E)$ achieved previously for the simple modules over the Toeplitz algebra.

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Gene Abrams, Francesca Mantese, Alberto Tonolo. 2022-07-07. Injectives over Leavitt path algebras of graphs with disjoint cycles. https://arxiv.org/abs/2207.03419

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