Injectives over Leavitt path algebras of graphs with disjoint cycles

2022/07/07 by Abrams, Gene, Mantese, Francesca, Tonolo, Alberto
#16S88 #16S99 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2207.03419

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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