{"paper":{"title":"Transposition anti-involution in Clifford algebras and invariance groups of scalar products on spinor spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Bertfried Fauser, Rafal Ablamowicz","submitted_at":"2011-12-13T21:19:50Z","abstract_excerpt":"We introduce on the abstract level in real Clifford algebras \\cl_{p,q} of a non-degenerate quadratic space (V,Q), where Q has signature \\epsilon=(p,q), a transposition anti-involution \\tp. In a spinor representation, the anti-involution \\tp gives transposition, complex Hermitian conjugation or quaternionic Hermitian conjugation when the spinor space \\check{S} is viewed as a \\cl_{p,q}-left and \\check{K}-right module with \\check{K} isomorphic to R or R^2, C, or, H or H^2.\n  \\tp is a lifting to \\cl_{p,q} of an orthogonal involution \\tve: V \\rightarrow V which depends on the signature of Q. The in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.3047","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"}