The finitistic dimension conjecture for finite-dimensional algebras

Lineage and corrections

The Nakayama conjecture on dominant dimension evidence for this event

Lean proof (OAI.LittleFinitistic.extreme_left_right_asymmetry) evidence for this event

This event attributed to Unreleased internal OpenAI model

Comparator statement: FinitisticAsymmetry.lean evidence for this event

Comparator statement: LittleFinitistic.lean evidence for this event

The finitistic dimension conjecture for finite-dimensional algebras evidence for this event

VibeMathed record: The finitistic dimension conjecture for finite-dimensional algebras evidence for this event

The finitistic dimension conjecture for finite-dimensional algebras parent of this event

Lean proof (OAI.LittleFinitistic.Main.exists_counterexample) evidence for this event

Theorem 1.1: there is a finite-dimensional complex algebra $A$ with, for each $m\ge1$, a finite-dimensional left module $N_m$ with $2m-2\le\mathrm{pd}\,N_m<\infty$; so $\mathrm{findim}\,A=\infty$ and the big finitistic dimension is infinite too, refuting the conjecture for Artin algebras. By Rickard's theorem injective left $A$-modules do not generate the derived category. Corollary (left-right asymmetry): an algebra $\Lambda$ with both finitistic dimensions infinite on the left and zero on the right. The construction passes through a finitely presented group algebra with Abels-type central involutions. A companion OpenAI manuscript (Tachikawa family) independently gives characteristic-two examples. parent of this event