Theoretical analysis constructs projective resolutions for simple modules over Leavitt path algebras, revealing the dimension of module extension spaces.
Let K be any field, and let E be any graph. We explicitly construct the projective resolution of simple left modules over the Leavitt path algebra L K (E) associated to cycles and irreducible polynomials. Then we study the dimension of the K-vector space of the extensions between two such simple modules.
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Mantese et al. (2026) studied this question.
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