{"paper":{"title":"No dialgebra has Gelfand-Kirillov dimension strictly between 1 and 2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Bing Yu, Yuqun Chen, Zerui Zhang","submitted_at":"2019-04-26T07:46:42Z","abstract_excerpt":"The Gelfand-Kirillov dimension measures the asymptotic growth rate of algebras. For every associative dialgebra $\\mathcal{D}$, the quotient $\\mathcal{A}_\\mathcal{D}:=\\mathcal{D}/\\mathsf{Id}(S)$, where $\\mathsf{Id}(S)$ is the ideal of $\\mathcal{D}$ generated by the set $S:=\\{x \\vdash y-x\\dashv y \\mid x,y\\in \\mathcal{D}\\}$, is called the associative algebra associated to $\\mathcal{D}$. Here we show that the Gelfand--Kirillov dimension of $\\mathcal{D}$ is bounded above by twice the Gelfand--Kirillov dimension of $\\mathcal{A}_\\mathcal{D}$. Moreover, we prove that no associative dialgebra has Gelfa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.12677","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"}