{"id":"openai-math/Relative-generation-and-the-generator-problem-for-finite-factors","pdf":"https://github.com/openai/math/blob/main/preprints/Relative-generation-and-the-generator-problem-for-finite-factors-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Relative-generation-and-the-generator-problem-for-finite-factors-September-23-2026","tags":["operator-algebras","von-neumann-algebras"],"score":0,"title":"Relative generation and the generator problem for finite factors","domain":"Operator algebras","family":"296","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.OA","summary":"We prove that every type II 1 factor with separable predual is generated by one operator, equivalently by two self-adjoint operators. Combined with the established direct-integral reduction to this case, this gives an affirmative solution of the generator problem for von Neumann algebras with separable predual.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":1,"published":"2026-09-23","reactions":{},"discussion":[{"url":"https://arxiv.org/abs/2610.28478","date":"2026-10-20","kind":"web","site":"arXiv.org","text":"In this note, assuming the finite factor generation theorem obtained by OpenAI, we demonstrate that if a separable simple unital $C^*$-algebra $A$ with nonempty trace space, has the strict comparison for positive elements, and its uniform tracial completion has complemented partitions of unity…","added":"2026-10-24","title":"A single generation theorem for simple unital $C^*$-algebras with CPoU and comparison","author":"Xin Ma","record":"arxiv/2610.28478"}],"formalized":true,"family_title":"The generator problem for finite factors"}