{"paper":{"title":"${\\mathbb Z}_2 \\times {\\mathbb Z}_2 $ generalizations of ${\\cal N} = 2$ super Schr\\\"odinger algebras and their representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"J. Segar, N. Aizawa","submitted_at":"2017-05-29T23:19:14Z","abstract_excerpt":"We generalize the real and chiral $ {\\cal N} =2 $ super Schr\\\"odinger algebras to ${\\mathbb Z}_2 \\times {\\mathbb Z}_2$-graded Lie superalgebras. This is done by $D$-module presentation and as a consequence, the $D$-module presentations of ${\\mathbb Z}_2 \\times {\\mathbb Z}_2$-graded superalgebras are identical to the ones of super Schr\\\"odinger algebras. We then generalize the calculus over Grassmann number to ${\\mathbb Z}_2 \\times {\\mathbb Z}_2 $ setting. Using it and the standard technique of Lie theory, we obtain a vector field realization of ${\\mathbb Z}_2 \\times {\\mathbb Z}_2$-graded super"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.10414","kind":"arxiv","version":2},"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"}