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Unipotent tensor categories and pronilpotent Lie quasibialgebras

Primarily AI-generated textHuman understanding: some partsmath.QA — Quantum Algebramath.CT — Category Theory

Contributed by Pavel I Etingof ↗

Version 1 / Oct 14, 2026 / CC BY 4.0

Abstract

We construct a bijection between tensor equivalence classes of unipotent tensor categories over $\C$ and continuous Lie quasibialgebras with linearly compact pronilpotent underlying Lie algebra, modulo continuous isomorphisms and classical twists. The bijection is defined using a fixed universal quantization functor and solves the problem raised in Remark~4.6 of arXiv:0708.1487 by Etingof and Gelaki. The proof combines reconstruction with filtered dequantization modulo twists and convergence of universal formulas. A category admits a tensor fiber functor precisely when a classical twist removes its curvature.

Provenance statement

This text has been produced by ChatGPT at a request by Pavel Etingof. It was repeatedly checked by AI agents (both ChatGPT and Claude) and revised to their satisfaction. Pavel's prompt is included at the end.

Tools used

Anthropic
Claude FableVersion 5
OpenAI
ChatGPTVersion 6 Pro

References

  1. P. Etingof and S. Gelaki, Quasisymmetric and unipotent tensor categories , Math. Res. Lett.\ 15 (2008), no. 5, 857--866; arXiv:0708.1487v2 (https://arxiv.org/abs/0708.1487v2).arXiv
  2. P. Etingof, S. Gelaki, D. Nikshych, and V. Ostrik, Tensor Categories , Mathematical Surveys and Monographs, vol. 205, American Mathematical Society, Providence, RI, 2015. Author's final version (https://math.mit.edu/~etingof/egnobookfinal.pdf).link
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Version history

  1. v1Submitted by Pavel I EtingofInitial depositCurrentOct 14, 2026