Open Research Index

Counterexamples to the weakly Gorenstein symmetry conjecture

Qiyue Tang

Hexagonhexagon/2610.00436Oct 21, 2026math.RTAI-generatedscore 0

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.

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