{"paper":{"title":"The Asymptotic Behavior of the Codimension Sequence of Affine G - Graded Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Yuval Shpigelman","submitted_at":"2015-04-01T20:07:19Z","abstract_excerpt":"Let W be an affine PI algebra over a field of characteristic zero graded by a finite group G. We show that there exist $\\alpha_{1},\\alpha_{2}\\in\\mathbb{R}, \\beta\\in\\frac{1}{2}\\mathbb{Z}$, and $l\\in\\mathbb{N}$ such that $\\alpha_{1}n^{\\beta}l^{n}\\leq c_{n}^{G}(W)\\leq\\alpha_{2}n^{\\beta}l^{n}$. Furthermore, if W has a unit then the asymptotic behavior of $c_{n}^{G}(W)$ is $\\alpha n^{\\beta}l^{n}$ where $\\alpha\\in\\mathbb{R}, \\beta\\in\\frac{1}{2}\\mathbb{Z}, l\\in\\mathbb{N}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.00373","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"}