{"paper":{"title":"Periodic algebras generated by groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RA","authors_text":"B. A. Omirov, S. Albeverio, U. A. Rozikov","submitted_at":"2011-11-16T10:51:32Z","abstract_excerpt":"We consider algebras with basis numerated by elements of a group $G.$ We fix a function $f$ from $G\\times G$ to a ground field and give a multiplication of the algebra which depends on $f$. We study the basic properties of such algebras. In particular, we find a condition on $f$ under which the corresponding algebra is a Leibniz algebra. Moreover, for a given subgroup $\\hat G$ of $G$ we define a $\\hat G$-periodic algebra, which corresponds to a $\\hat G$-periodic function $f,$ we establish a criterion for the right nilpotency of a $\\hat G$-periodic algebra. In addition, for $G=\\mathbb Z$ we des"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.3760","kind":"arxiv","version":3},"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"}