2017/02/22 by Marcos, Eduardo N., Moreira, Marcelo
#13D05 13D09 14F05 16D10 16E10 16E35 16G20 #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1702.06849
Let KΔ be the incidence algebra associated with a finite poset (Δ,\preceq) over the algebraically closed field K. We present a study of incidence algebras KΔ that are piecewise hereditary, which we denominate PHI algebras. We investigate the strong global dimension, the simply conectedeness and the one-point extension algebras over a PHI algebras. We also give a positive answer to the so-called Skowroński problem for KΔ a PHI algebra which is not of wild quiver type. That is for this kind of algebra we show that HH1(KΔ) is trivial if, and only if, KΔ is a simply connected algebra. We determine an upper bound for the strong global dimension of PHI algebras; furthermore, we extend this result to sincere algebras proving that the strong global dimension of a sincere piecewise hereditary algebra is less or equal than three.