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A reduction of the Gorenstein symmetry conjecture to gendo-symmetric algebras

A mix of human-written and AI-generated textHuman understanding: some partsmath.RT — Representation Theory

Contributed by Qiyue Tang

Version 2 / Oct 20, 2026 / CC BY 4.0

Abstract

We reduce the Gorenstein symmetry conjecture for Artin algebras to gendo-symmetric algebras relative to Artin duality

Provenance statement

Some of the results in this paper were obtained by AI. The result has passed Rethlas-OSV’s strong adversarial review (2-way parallel, reasoning intensity: astra-Xhigh).

References

  1. M. Auslander, I. Reiten and S. O. Smalø, Representation Theory of Artin Algebras , Cambridge Studies in Advanced Mathematics 36 , Cambridge University Press, 1995.
  2. T. Aihara, A. Chan and T. Honma, On the gendo-symmetric algebra of a trivial extension algebra , conference report, 2019, 6 pp. Author report (https://ring-theory-japan.com/ring/oldmeeting/2019/report2019/AIHARA-AARON-HONMA2.pdf).link
  3. H. Chen and S. Koenig, Ortho-symmetric modules, Gorenstein algebras and derived equivalences , preprint (2015), arXiv:1506.03337v1 (https://arxiv.org/abs/1506.03337v1).arXiv
  4. M. Fang and S. Koenig, Endomorphism algebras of generators over symmetric algebras , J. Algebra 332 (2011), 428--433. doi:10.1016/j.jalgebra.2011.02.031 (https://doi.org/10.1016/j.jalgebra.2011.02.031).DOI
  5. M. Fang and S. Koenig, Gendo-symmetric algebras, canonical comultiplication, bar cocomplex and dominant dimension , Trans. Amer. Math. Soc. 368 (2016), no. 7, 5037--5055. doi:10.1090/tran/6504 (https://doi.org/10.1090/tran/6504).DOI
  6. Y. Han and Y. Qin, Reducing homological conjectures by nn-recollements , preprint (2014), arXiv:1410.3223v2 (https://arxiv.org/abs/1410.3223v2).arXiv
  7. Y. Han, Y. Qin and X. Wang, Singular equivalences of nn-adjoint type and standard eventually homological isomorphisms , preprint (2026), arXiv:2609.03365v2 (https://arxiv.org/abs/2609.03365v2).arXiv
  8. W. Hu and C. Xi, Almost D\mathcal D-split sequences and derived equivalences , preprint (2008), arXiv:0810.4757v1 (https://arxiv.org/abs/0810.4757v1).arXiv

Version history

  1. v1Submitted by Qiyue TangInitial depositSupersededOct 19, 2026
  2. v2Submitted by Qiyue TangSubmitted as a new versionCurrentOct 27, 2026