A family of finite dimensional Hopf algebras over $\mathbb{C}$ with varying algebra structure

Pavel I Etingof

A family of finite dimensional Hopf algebras over $\mathbb{C}$ with varying algebra structure

Primarily AI-generated textHuman understanding: some partsmath.RA — Rings and Algebras math.CT — Category Theory

Contributed by Pavel I Etingof ↗

Version 1 / Nov 10, 2026 / CC BY 4.0

Abstract

We construct an algebraic one-parameter family of complex Hopf algebras of dimension

1024

, with fixed coalgebra, whose underlying associative algebras vary in a continuous family of isomorphism classes. Four multiplication lines in the second radical layer of a distinguished block recover the

j

-invariant of the elliptic curve given by the equation

y^2=x(x-1)(x-t^2).

This answers negatively the finiteness question of Etingof and Gelaki concerning algebra types of Hopf algebras of fixed dimension.

Provenance statement

This text has been produced by ChatGPT at a request by Pavel Etingof. It was repeatedly checked by AI agents and revised in response to their comments.

Tools used

OpenAI: ChatGPTVersion 6 Pro

References

P. Etingof and S. Gelaki, On families of triangular Hopf algebras , International Mathematics Research Notices 2002 , no. 14, 757--768. arXiv:math/0110043 (https://arxiv.org/abs/math/0110043).arXiv

Version history

v1 · 8 pagesSubmitted by Pavel I EtingofInitial depositCurrentNov 08, 2026