{"id":"palomar/PALOMAR-2026-09-30-000024","url":"https://github.com/stalex444/pdt-hodge-lie-generation/tree/e2d8dde6f076b730b9a718c95ff1664c6aa88b51","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-09-30-000024-v1.json","repo":"https://github.com/stalex444/pdt-hodge-lie-generation","tags":["math.RT","msc:17B05","msc:17B10","lie-algebras","representation-theory","sl-n"],"score":0,"title":"Local Hodge generation of sl(15) and scalar response rigidity","trust":"high","domain":"math.RT","source":"palomar","authors":["Stephanie Alexander"],"reviews":0,"subject":"math.RT","summary":"An explicit local Hodge operator on the oriented coordinate four-plane 0123, extended by zero, together with the fifteen adjoint basis actions of the orthogonal algebra for diag(1,1,1,-1,1,-1), generates sl(15,K) over every field of characteristic different from two. A finite integral commutator certificate produces signed skew matrix units and one symmetric seed; a general propagation lemma then produces all trace-free matrices. Dimension 224 follows from generation. As a consequence, an endomorphism of this algebra commuting with the commutator actions of the same sixteen generators is…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-09-30","reactions":{},"formalized":true}