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We consider antiunitary representations $U$ of the Lie group $G_\\tau = G \\rtimes \\{e,\\tau_G\\}$ for which the positive cone $C_U = \\{ x \\in \\mathfrak{g} : -i \\partial U(x) \\geq 0\\}$ and $h$ span $\\mathfrak{g}$. To a real subspace E of distribution vectors invariant under $exp(\\mathbb{R} h)$ and an open subset $O \\subseteq G$, we associate the"},"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":"2006.09832","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2020-06-16T14:59:35Z","cross_cats_sorted":["math.MP","math.OA","math.RT"],"title_canon_sha256":"202066f572a1b5b7364ff5c2a67fa0fddc477eba49a811c1c7959914cc17cd69","abstract_canon_sha256":"ef30beeaf9b3ebf40d090541c0ad2e8f2efd6b918566d058c79e4a9bf1e456d3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:12:49.625984Z","signature_b64":"Mo85s6Mpwrbko2LLv02fiw50VfY4yNQOV6BiHZ4B8og3jclPtQKiZEkqUM9VHgJRqe6LgeB/4GLCOZMRr44nAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"19c8758a0707c7f90b5c410bae3486a5610304c2345fc9724fa9906c1c44d052","last_reissued_at":"2026-07-05T01:12:49.625618Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:12:49.625618Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nets of standard subspaces on Lie groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.OA","math.RT"],"primary_cat":"math-ph","authors_text":"Gestur Olafsson, Karl-Hermann Neeb","submitted_at":"2020-06-16T14:59:35Z","abstract_excerpt":"Let G be a Lie group with Lie algebra $\\mathfrak{g}$, $h \\in \\frak{g}$ an element for which the derivation ad(h) defines a 3-grading of $\\mathfrak{g}$ and $\\tau_G$ an involutive automorphism of G inducing on $\\mathfrak{g}$ the involution $e^{\\pi i ad(h)}$. We consider antiunitary representations $U$ of the Lie group $G_\\tau = G \\rtimes \\{e,\\tau_G\\}$ for which the positive cone $C_U = \\{ x \\in \\mathfrak{g} : -i \\partial U(x) \\geq 0\\}$ and $h$ span $\\mathfrak{g}$. 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