{"paper":{"title":"Piecewise Hereditary Incidence Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Eduardo N. Marcos, Marcelo Moreira","submitted_at":"2017-02-22T15:34:35Z","abstract_excerpt":"Let $K\\Delta$ be the incidence algebra associated with a finite poset $(\\Delta,\\preceq)$ over the algebraically closed field $K$. We present a study of incidence algebras $K\\Delta$ 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.\n  We also give a positive answer to the so-called Skowro\\'nski problem for $K\\Delta$ a PHI algebra which is not of wild quiver type. That is for this kind of algebra we show that $HH^1(K\\Delta)$ is trivial if, and only if, $K\\D"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.06849","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}