2014/08/15 by Gene Abrams, Abrams, Gene, Francesca Mantese +3
Mathematics · #16S99 #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:16S99
paper · pdf · doi:10.48550/arxiv.1408.3580
updated: dedication to Alberto Facchini on the occasion of his 60th Birthday added in front matter
arxiv created 2015/01/19 · arxiv updated 2015/01/20
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 \rm ExtLK(E)1(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.