{"paper":{"title":"Categorification of sign-skew-symmetric cluster algebras and some conjectures on g-vectors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.RA"],"primary_cat":"math.RT","authors_text":"Fang Li, Min Huang, Peigen Cao","submitted_at":"2017-04-25T06:30:10Z","abstract_excerpt":"Using the unfolding method given in \\cite{HL}, we prove the conjectures on sign-coherence and a recurrence formula respectively of ${\\bf g}$-vectors for acyclic sign-skew-symmetric cluster algebras. As a following consequence, the conjecture is affirmed in the same case which states that the ${\\bf g}$-vectors of any cluster form a basis of $\\mathbb Z^n$. Also, the additive categorification of an acyclic sign-skew-symmetric cluster algebra $\\mathcal A(\\Sigma)$ is given, which is realized as $(\\mathcal C^{\\widetilde Q},\\Gamma)$ for a Frobenius $2$-Calabi-Yau category $\\mathcal C^{\\widetilde Q}$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.07549","kind":"arxiv","version":2},"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"}