{"paper":{"title":"The Igusa-Todorov $\\phi$ function for truncated path algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Gustavo Mata, Gustavo Rama, Marcos Barrios","submitted_at":"2017-07-15T18:30:52Z","abstract_excerpt":"Given a truncated path algebra $A=\\frac{\\Bbbk Q}{J^k}$ we prove that $\\fidim A = \\fidim A^{\\op}$. We also compute the $\\phi$-dimension of $A$ in function of the $\\phi$-dimension of $\\frac{\\Bbbk Q}{J^2}$ when $Q$ has no sources nor sinks. This allows us to bound the $\\phi$-dimension for truncated path algebras. Finally, we characterize $A$ when its $\\phi$-dimension is equal to $1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.04774","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"}