{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"b97e6c67401e7b33124424136e40fc3a03bb1260544c3e2e89217e5d85fcb846","created":"2026-10-03T07:18:09Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"13a59c2e0b0bb07a1bceae97933d0b3531a13bcc5b11b1605eb58c616e3bed7b","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"identification","assisted_by":[],"external_id":"qft.double-copy.kinematic-algebra","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[],"plain":"Color factors come from a known algebra, the rules for combining color charges. The matching algebra for the momentum-dependent parts is known only for a simplified self-dual sector of the theory.","posed_since":"2011","precise":"Identify an infinite-dimensional Lie algebra with structure constants $F$ such that tree-level BCJ numerators of $D$-dimensional Yang-Mills at all multiplicities are nested products of F with the same graph structure as nested color factors $f^{abc}$. In the self-dual sector the algebra is that of area-preserving diffeomorphisms (Monteiro and O'Connell, 2011); an answer is the algebra for the full theory, or a proof that no Lie algebra (as opposed to a Hopf, homotopy or other structure) can do this.","problem_ref":null,"references":"","settled_by":"An explicit algebra reproducing tree-level Yang-Mills numerators at all multiplicities, or a no-go proof.","status_note":"Kinematic Hopf-algebra constructions (from 2021) generate tree-level BCJ numerators, and homotopy-algebra work (Bonezzi, Chiaffrino, Diaz-Jaramillo, Hohm, arXiv:2212.04513, 2023) finds a generalized Batalin-Vilkovisky algebra in off-shell Yang-Mills; no strict Lie algebra for the full theory is known as of 2026.","title":"Kinematic Lie algebra of full Yang-Mills theory","topic_ref":"1423f8d1d6c45d6696107efe735144c4230462c57b3f02acac8489226faee33e"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"3bfc628f6dc9d4264017cf6380f6886472bdaa4175b46e80b5627ddc9ca0598f","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"b0bb47e2b15425fee593ece14786bf9b15fd83cbdad4c2b6d0e5543f646c4caf","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"uDZEJfA4YVMdPpE0ccNiaY-ouAlo7sml0wxQ_gnwFUqWMJOJYCcsFp3C7f9P94Jie5d79yEo79I6izQObF6dCg"},"schema":"pubphys.envelope/1"},"record_hash":"3bfc628f6dc9d4264017cf6380f6886472bdaa4175b46e80b5627ddc9ca0598f","leaf_index":1907}