{"paper":{"title":"$\\mathbb{Z}_2^n$-Supergeometry I: Manifolds and Morphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AG","math.MP","math.QA"],"primary_cat":"math.DG","authors_text":"Janusz Grabowski, Norbert Poncin, Tiffany Covolo","submitted_at":"2014-08-12T15:56:10Z","abstract_excerpt":"In Physics and in Mathematics $\\mathbb{Z}_2^n$-gradings, $n \\geq 2$, do appear quite frequently. The corresponding sign rules are determined by the `scalar product' of the involved $\\mathbb{Z}_2^n$-degrees. The present paper is the first of a series on $\\mathbb{Z}_2^n$-Supergeometry. The new theory exhibits challenging differences with the classical one: nonzero degree even coordinates are not nilpotent, and even (resp., odd) coordinates do not necessarily commute (resp., anticommute) pairwise (the parity is the parity of the total degree). It is based on the hierarchy: ` $\\mathbb{Z}_2^0$-Supe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.2755","kind":"arxiv","version":2},"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"}