{"paper":{"title":"Isomorphism problem and homological properties of DG free algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Almire. Abla, J.-F. Xie, X.-F. Mao, Y.-N. Yang","submitted_at":"2018-05-05T05:20:27Z","abstract_excerpt":"A differential graded (DG for short) free algebra $\\mathcal{A}$ is a connected cochain DG algebra such that its underlying graded algebra is $$\\mathcal{A}^{\\#}=\\k\\langle x_1,x_2,\\cdots, x_n\\rangle,\\,\\, \\text{with}\\,\\, |x_i|=1,\\,\\, \\forall i\\in \\{1,2,\\cdots, n\\}.$$ We prove that the differential structures on DG free algebras are in one to one correspondence with the set of crisscross ordered $n$-tuples of $n\\times n$ matrixes. We also give a criterion to judge whether two DG free algebras are isomorphic.\n  As an application, we consider the case of $n=2$. Based on the isomorphism classificatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.02001","kind":"arxiv","version":1},"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"}