Let E be a directed graph, K any field, and let LK(E) denote the Leavitt path algebra of E with coefficients in K. For each rational infinite path c∞ of E we explicitly construct a projective resolution of the corresponding Chen simple left LK(E)-module V[c∞]. Further, when E is row- finite, for each irrational infinite path p of E we explicitly construct a projective resolution of the corresponding Chen simple left LK(E)-module V[p]. For Chen simple modules S, T we describe Ext1LK (E)(S, T ) by presenting an explicit K-basis. For any graph E containing at least one cycle, this description guarantees the existence of indecomposable left LK(E)-modules of any prescribed finite length.

Extensions of simple modules over Leavitt path algebras

MANTESE, Francesca;
2015

Abstract

Let E be a directed graph, K any field, and let LK(E) denote the Leavitt path algebra of E with coefficients in K. For each rational infinite path c∞ of E we explicitly construct a projective resolution of the corresponding Chen simple left LK(E)-module V[c∞]. Further, when E is row- finite, for each irrational infinite path p of E we explicitly construct a projective resolution of the corresponding Chen simple left LK(E)-module V[p]. For Chen simple modules S, T we describe Ext1LK (E)(S, T ) by presenting an explicit K-basis. For any graph E containing at least one cycle, this description guarantees the existence of indecomposable left LK(E)-modules of any prescribed finite length.
Leavitt path algebras, modules, extension
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11562/933001
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