{"paper":{"title":"Non-degeneracy of Killing forms on real conjugacy classes of finite groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GR","authors_text":"Carsten Dietzel, Charlotte Roelants","submitted_at":"2026-05-28T17:50:37Z","abstract_excerpt":"Killing forms on finite groups arise as special cases of braided Killing forms on braided Lie algebras. If $\\mathcal{C}$ is a conjugation-stable subset of a finite group $G$, the Killing form on $\\mathbb{C}\\mathcal{C}$ is given by $K_\\mathcal{C}(a,b) = |C_G(ab) \\cap \\mathcal{C}|$ for $a,b \\in \\mathcal{C}$. It is conjectured in previous work by L\\'opez Pe\\~na, Majid and Rietsch that $K_\\mathcal{C}$ is non-degenerate for any real conjugacy class $\\mathcal{C}$ in a finite simple group.\n  In this article, we reformulate the conjecture and introduce combinatorial conditions - the $\\textit{1-element"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.30408","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.30408/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}