{"paper":{"title":"Twist invariants of graded algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"K.R. Goodearl, M.T. Yakimov","submitted_at":"2017-06-21T15:31:00Z","abstract_excerpt":"We define two invariants for (semiprime right Goldie) algebras, one for algebras graded by arbitrary abelian groups, which is unchanged under twists by $2$-cocycles on the grading group, and one for $\\mathbb Z$-graded or $\\mathbb Z_{\\ge 0}$-filtered algebras. The first invariant distinguishes quantum algebras which are \"truly multiparameter\" apart from ones that are \"essentially uniparameter\", meaning cocycle twists of uniparameter algebras. We prove that both invariants are stable under adjunction of polynomial variables. Methods for computing these invariants for large families of algebras a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.06957","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"}