{"paper":{"title":"Clifford Parallelisms and External Planes to the Klein quadric","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.AG","authors_text":"Hans Havlicek","submitted_at":"2015-11-19T18:57:51Z","abstract_excerpt":"For any three-dimensional projective space ${\\mathbb P}(V)$, where $V$ is a vector space over a field $F$ of arbitrary characteristic, we establish a one-one correspondence between the Clifford parallelisms of ${\\mathbb P}(V)$ and those planes of ${\\mathbb P}(V\\wedge V)$ that are external to the Klein quadric representing the lines of ${\\mathbb P}(V)$. We also give two characterisations of a Clifford parallelism of ${\\mathbb P}(V)$, both of which avoid the ambient space of the Klein quadric."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.06308","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"}