{"paper":{"title":"Prime (-1,1) and Jordan monsters and superalgebras of vector type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Ivan P. Shestakov, Sergey V. Pchelintsev","submitted_at":"2013-11-29T14:59:58Z","abstract_excerpt":"It is proved that the prime degenerate (-1,1) algebra constructed in [13] (the (-1,1)-monster) generates the same variety of algebras as the Grassman (-1,1)-algebra. Moreover, the same variety is generated by the Grassmann envelope of any simple nonassociative (-1,1)-superalgebra. The variety occurs to be the smallest variety of (-1,1)-algebras that contains prime nonassociative algebras. Similar results are obtained for Jordan algebras. Thus, the Jordan monster (the prime degenerate algebra constructed in [13]) and the Grassmann envelope of the prime Jordan superalgebra of vector type have th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.7587","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"}