{"paper":{"title":"A supercharacter theory for involutive algebra groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Ana Margarida Neto, Carlos A. M. Andr\\'e, Pedro J. Freitas","submitted_at":"2015-02-05T11:57:44Z","abstract_excerpt":"If $\\mathscr{J}$ is a finite-dimensional nilpotent algebra over a finite field $\\Bbbk$, the algebra group $P = 1+\\mathscr{J}$ admits a (standard) supercharacter theory as defined by Diaconis and Isaacs. If $\\mathscr{J}$ is endowed with an involution $\\widehat{\\varsigma}$, then $\\widehat{\\varsigma}$ naturally defines a group automorphism of $P = 1+\\mathscr{J}$, and we may consider the fixed point subgroup $C_{P}(\\widehat{\\varsigma}) = \\{x\\in P : \\widehat{\\varsigma}(x) = x^{-1}\\}$. Assuming that $\\Bbbk$ has odd characteristic $p$, we use the standard supercharacter theory for $P$ to construct a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.01512","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"}