{"id":"hexagon/2610.00436","pdf":"https://hexagonmath.org/pdf/2610.00436v1","url":"https://hexagonmath.org/abs/2610.00436v1","tags":["msc:16E65","msc:16G10","weakly Gorenstein symmetry conjecture"],"score":0,"title":"Counterexamples to the weakly Gorenstein symmetry conjecture","domain":"math.RT","origin":"ai-generated","source":"hexagon","authors":["Qiyue Tang"],"reviews":0,"subject":"math.RT","summary":"We construct a 29-dimensional algebra which is left weakly Gorenstein and is not right weakly Gorenstein. We also construct a 145-dimensional gendo-symmetric algebra with the same property. Both constructions work over every field containing an element of infinite multiplicative order. These examples disprove the weakly Gorenstein symmetry conjecture.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-21","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}