OpenAI reports an Auslander–Reiten counterexample for Artin algebras
- Mathematics
A finite-dimensional algebra over F₂(q,H₁,H₂) has a finite-dimensional nonprojective Gorenstein-projective module Z with Extⁱ(Z,Z)=Extⁱ(Z,Λ)=0 for every i>0.
OpenAI reports an Auslander–Reiten counterexample for Artin algebras
- Mathematics
A finite-dimensional algebra over F₂(q,H₁,H₂) has a finite-dimensional nonprojective Gorenstein-projective module Z with Extⁱ(Z,Z)=Extⁱ(Z,Λ)=0 for every i>0.
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Read the background
A finite-dimensional algebra over F₂(q,H₁,H₂) has a finite-dimensional nonprojective Gorenstein-projective module Z with Extⁱ(Z,Z)=Extⁱ(Z,Λ)=0 for every i>0.
Why it matters
If correct, disproves the unrestricted Auslander–Reiten conjecture for Artin algebras and its Gorenstein-projective variant.
What counts as progress
Must vanishing self-Ext and Ext against an Artin algebra force a module to be projective?
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OpenAI reports an Auslander–Reiten counterexample for Artin algebras