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Disproof of Xi’s conjecture on the representation dimension of idempotent corners

A mix of human-written and AI-generated textHuman understanding: some partsmath.RT — Representation Theorymath.RA — Rings and Algebras

Contributed by Qiyue Tang ↗

Version 1 / Nov 07, 2026 / CC BY 4.0

Abstract

We disprove Xi’s conjecture on the representation dimension of idempotent corners. Over every field and for each integer (L\ge3), we construct an algebra of representation dimension (L+1) with a corner of representation dimension (2L-1).

Provenance statement

The main results of this paper were generated using GPT-6 Pro in an eight-hour research run on 5 November 2026. Codex was used to review the proofs and revise the exposition.This article has also passed the Rethlas-OSV review.

References

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  1. A. Zhang and S. Zhang, On the finitistic dimension conjecture of Artin algebras , J. Algebra 320 (2008), 253--258.

Version history

  1. v1 · 19 pagesSubmitted by Qiyue TangRevised after moderator-requested changesCurrentNov 07, 2026