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A fourteen-dimensional biperfect Lie bialgebra

Primarily AI-generated textHuman understanding: some partsmath.QA — Quantum Algebra

Contributed by Pavel I Etingof ↗

Version 1 / Oct 16, 2026 / CC BY 4.0

Abstract

We construct a fourteen-dimensional Lie bialgebra for which both the underlying Lie algebra and its dual are perfect. The construction is defined over Q\mathbb{Q} and is self-dual over C\mathbb{C}. It gives an affirmative answer to Question 4.1(3) of Etingof--Gelaki--Guralnick--Saxl, arXiv:9912068. Its twenty-eight-dimensional Drinfeld double is quasitriangular with injective cobracket, also answering Question 4.1(4).

Provenance statement

This paper was written by ChatGPT 6 Pro in response to the following prompt by Pavel Etingof: "Is there a nonzero finite-dimensional Lie bialgebra $\g$ over $\mathbb C$ for which both $\g$ and $\g^*$ are perfect?"

Tools used

OpenAI
ChatGPTVersion 6 Pro

References

  1. V. G. Drinfeld, Quantum groups , Proceedings of the International Congress of Mathematicians, Berkeley, 1986, Vol. 1, Amer. Math. Soc., Providence, RI, 1987, pp. 798--820. Full text (https://ncatlab.org/nlab/files/Drinfeld-QuantumGroups.pdf).link
  2. P. Etingof, S. Gelaki, R. Guralnick, and J. Saxl, Biperfect Hopf algebras , arXiv:math/9912068 (1999). https://arxiv.org/abs/math/9912068.arXiv
  3. A. Medina and P. Revoy, Algèbres de Lie et produit scalaire invariant , Ann. Sci. École Norm. Sup. (4) 18 (1985), no. 3, 553--561. doi:10.24033/asens.1496 (https://doi.org/10.24033/asens.1496).DOI

Version history

  1. v1Submitted by Pavel I EtingofInitial depositCurrentOct 16, 2026