{"paper":{"title":"Complete classification of pseudo $H$-type algebras: II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Irina Markina, Kenro Furutani","submitted_at":"2017-03-15T06:08:13Z","abstract_excerpt":"We classify a class of 2-step nilpotent Lie algebras related to the representations of the Clifford algebras in the following way. Let $J\\colon \\Cl(\\mathbb R^{r,s})\\toU$ be a representation of the Clifford algebra $\\Cl(\\mathbb R^{r,s})$ generated by the pseudo Euclidean vector space $\\mathbb R^{r,s}$. Assume that the Clifford module $U$ is endowed with a bilinear symmetric non-degenerate real form $\\la\\cdot\\,,\\cdot\\ra_U$ making the linear map $J_z$ skew symmetric for any $z\\in\\mathbb R^{r,s}$. The Lie algebras and the Clifford algebras are related by $\\la J_zv,w\\ra_U=\\la z,[v,w]\\ra_{\\mathbb R^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.04948","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"}