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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^"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1703.04948","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-03-15T06:08:13Z","cross_cats_sorted":[],"title_canon_sha256":"d45c90d1e6d644f75bb30d55a2da586de769b425a0eb78fd411636b9faf476c9","abstract_canon_sha256":"d965b2bb901348b4c3b8ef81dc0f9b990cc6dbf6156f002b121ad9683f63b4cf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:38.786747Z","signature_b64":"asmAhpJRYKvvtvlxgsEGMiDh1z3ARYcByB0BAiQ1lN43ZdVSsfaf7IvBNsNyeIZK0LIC03OBqn1DYvsN9MSyAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"181093e13e65d1b3ce1aedde539023dfedd7eaf51e7d6d7b6f297f305188fc64","last_reissued_at":"2026-05-18T00:48:38.786057Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:38.786057Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $z\\in\\mathbb R^{r,s}$. 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