Gene Abrams

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math.RA2026

The injective envelope of simple modules over Leavitt path algebras II: simples arising from exclusive cycles

G. Abrams, F. Mantese, A. Tonolo

Let $K$ be any field, $E$ any directed graph, and $L_{K} (E)$ the associated Leavitt path algebra. As described first by Chen, and subsequently generalized by Ara and Rangaswamy, for…

math.RA2026

The injective envelope of simple modules over Leavitt path algebras I: simple left ideals

G. Abrams, F. Mantese, A. Tonolo

Let $K$ be any field and $E$ any directed graph. We characterize up to isomorphism the simple (i.e., minimal) left ideals of the Leavitt path algebra $L_{K} (E)$ . Then, for each simpl…

math.RA2023

Recasting the Hazrat Conjecture: Relating Shift Equivalence to Graded Morita Equivalence

Gene Abrams, Efren Ruiz, Mark Tomforde

Let $E$ and $F$ be finite graphs with no sinks, and $k$ any field. We show that shift equivalence of the adjacency matrices $A_{E}$ and $A_{F}$ , together with an additional compatibili…