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Another Counterexample to Little Finitistic Dimension Conjecture

Primarily AI-generated textHuman understanding: some partsmath.RA — Rings and Algebras

Contributed by Andy Jiang ↗

Version 1 / Oct 14, 2026 / CC BY 4.0

Abstract

A characteristic-zero counterexample to the Little Finitistic Dimension Conjecture is given, arguably providing a simpler variant of OpenAI's construction.

Provenance statement

Produced in conversation with GPT 6. I have not checked the relevant representation theory inputs.

References

  1. OpenAI, An algebra of infinite little finitistic dimension , OpenAI Math preprint, September 23, 2026. Preprint (https://github.com/openai/math/blob/main/preprints/An-algebra-of-infinite-little-finitistic-dimension-September-23-2026/paper.pdf).link
  2. Qiyue Tang, A note of refinements to an algebra of infinite little finitistic dimension , Hexagon, 2026. hexagon:2610.00140v4 (https://hexagonmath.org/2610.00140v4).hexagon
  3. Hiroyuki Minamoto and Kota Yamaura, Homological dimension formulas for trivial extension algebras , Journal of Pure and Applied Algebra 224 (2020), no. 8, 106344. arXiv:1710.01469 (https://arxiv.org/abs/1710.01469).arXiv
  4. L. Le Bruyn and S. P. Smith, Homogenized $\slie_2$ , Proceedings of the American Mathematical Society 118 (1993), 725--730, 2. Author's PDF (https://sites.math.washington.edu/~smith/Research/Homog-sl2.pdf).link
  5. L. Le Bruyn, S. P. Smith, and M. Van den Bergh, Central extensions of three dimensional Artin--Schelter regular algebras , Mathematische Zeitschrift 222 (1996), 171--212, Corollary 2.7 and Remark 2.8. Author's PDF (https://sites.math.washington.edu/~smith/Research/Central-extns.pdf).link
  6. H. Minamoto and I. Mori, Structures of AS-regular algebras , Propositions 4.3--4.4 and Theorem 4.12. Author's preprint (https://www.math.kyoto-u.ac.jp/preprint/2010/06Minamoto.pdf).link

Version history

  1. v1Submitted by Andy JiangInitial depositCurrentOct 14, 2026