{"paper":{"title":"On the generalized Clifford algebra of a monic polynomial","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Adam Chapman, Jung-Miao Kuo","submitted_at":"2014-06-08T13:08:19Z","abstract_excerpt":"In this paper we study the generalized Clifford algebra defined by Pappacena of a monic (with respect to the first variable) homogeneous polynomial $\\Phi(Z,X_1,\\dots,X_n)=Z^d-\\sum_{k=1}^d f_k(X_1,\\dots,X_n) Z^{d-k}$ of degree $d$ in $n+1$ variables over some field $F$. We completely determine its structure in the following cases: $n=2$ and $d=3$ and either $\\operatorname{char}(F)=3$, $f_1=0$ and $f_2(X_1,X_2)=e X_1 X_2$ for some $e \\in F$, or $\\operatorname{char}(F) \\neq 3$, $f_1(X_1,X_2)=r X_2$ and $f_2(X_1,X_2)=e X_1 X_2+t X_2^2$ for some $r,t,e \\in F$. Except for a few exceptions, this alge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.1981","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"}