{"paper":{"title":"Invariant theory in exterior algebras and Amitsur-Levitzki type theorems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Minoru Itoh","submitted_at":"2014-04-08T01:13:34Z","abstract_excerpt":"This article discusses invariant theories in some exterior algebras, which are closely related to Amitsur-Levitzki type theorems.\n  First we consider the exterior algebra on the vector space of square matrices of size $n$, and look at the invariants under conjugations. We see that the algebra of these invariants is isomorphic to the exterior algebra on an $n$-dimensional vector space. Moreover we give a Cayley-Hamilton type theorem for these invariants (the anticommutative version of the Cayley-Hamilton theorem). This Cayley-Hamilton type theorem can also be regarded as a refinement of the Ami"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1980","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"}