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By means of a global Lifting method for homogeneous operators proved by Folland in [On the Rothschild-Stein lifting theorem, Comm. PDEs, 1977], there exists a Carnot group $\\mathbb{G}$ and a polynomial surjective map $\\pi:\\mathbb{G}\\to \\mathbb{R}^n$ such that $\\mathcal{L}$ is $\\pi$-related to a sub-Laplacian $\\mathcal{L}_{\\mathbb{G}}$ on $\\mathbb{G}$. We show that it is always possible "},"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":"1604.02599","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-09T19:40:44Z","cross_cats_sorted":[],"title_canon_sha256":"698854f8bfe519e2a3861ad8b7a5305414e715b67ce6f8aa6acce874a0104e01","abstract_canon_sha256":"26f51dbd232668e6f2d36537a8e16b1d8e1c353d6847b3048603458cebdc6f3f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:06.597692Z","signature_b64":"iEqVj5QzwDKRSfruFcCZqX2fGGmfb2MG+MUAMm0dh/7RWyIrAryW+O77fT27UX8YPqFIS7SBlChRPfzcBHxLDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"29eeea383d5b315074d6d98506d4a06abf9be182bf7847ab8179cd36f108c938","last_reissued_at":"2026-05-18T00:45:06.597361Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:06.597361Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The existence of a global fundamental solution for homogeneous H\\\"ormander operators via a global lifting method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andrea Bonfiglioli, Stefano Biagi","submitted_at":"2016-04-09T19:40:44Z","abstract_excerpt":"We prove the existence of a global fundamental solution $\\Gamma(x;y)$ (with pole $x$) for any H\\\"ormander operator $\\mathcal{L}=\\sum_{i=1}^m X_i^2$ on $\\mathbb{R}^n$ which is $\\delta$-homogeneous of degree $2$. By means of a global Lifting method for homogeneous operators proved by Folland in [On the Rothschild-Stein lifting theorem, Comm. PDEs, 1977], there exists a Carnot group $\\mathbb{G}$ and a polynomial surjective map $\\pi:\\mathbb{G}\\to \\mathbb{R}^n$ such that $\\mathcal{L}$ is $\\pi$-related to a sub-Laplacian $\\mathcal{L}_{\\mathbb{G}}$ on $\\mathbb{G}$. 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