{"paper":{"title":"Complete classification of $H$-type algebras: I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Irina Markina, Kenro Furutani","submitted_at":"2015-12-10T22:31:43Z","abstract_excerpt":"Let $\\mathscr N$ be a 2-step nilpotent Lie algebra endowed with non-degenerate scalar product $\\langle.\\,,.\\rangle$ and let $\\mathscr N=V\\oplus_{\\perp}Z$, where $Z$ is the centre of the Lie algebra and $V$ its orthogonal complement with respect to the scalar product. We study the classification of the Lie algebras for which the space $V$ arises as a representation space of a Clifford algebra $\\Cl(\\mathbb R^{r,s})$ and the representation map $J\\colon \\Cl(\\mathbb R^{r,s})\\to(V)$ is related to the Lie algebra structure by $\\langle J_zv,w\\rangle=\\langle z,[v,w]\\rangle$ for all $z\\in \\mathbb R^{r,s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.03469","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"}