{"id":"hexagon/2610.00213","pdf":"https://hexagonmath.org/pdf/2610.00213v2","url":"https://hexagonmath.org/abs/2610.00213v2","tags":["math.OA","math-ph","msc:81T40","msc:17B69","msc:18M20","Fusion categories","vertex operator algebra"],"score":0,"title":"An order-five Haagerup--Izumi vertex operator algebra at central charge eight","domain":"math.QA","origin":"ai-generated","source":"hexagon","authors":["Tzu Chen Huang"],"reviews":0,"subject":"math.QA","summary":"We construct an explicit unitary strongly rational vertex operator algebra $U$ of central charge eight inside $V_{A_4\\oplus A_4}$ and identify $Rep(U)$ with the Drinfeld center of the positive order-five Haagerup--Izumi category. The construction adjoins one algebraic weight-two field to a diagonal affine $\\mathfrak{sl}_2$ at level forty and the ambient conformal vector. Exact finite lattice identities imply strong generation and $C_2$-cofiniteness. A finite integral order in the actual Zhu algebra descends semisimplicity from a $1590$-dimensional upper presentation over $\\mathbb F_{10069}$.…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["NumPy","SymPy","gmpy2","FLINT","GMP","GAP","SL2Reps","SciPy","mpmath"],"discussed":0,"published":"2026-10-13","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}