Two-Valued Groups, Chazy Equation, Dubrovin-Frobenius Structures, and QYBE
Algebraic Geometry
2026-04-30 v1 Mathematical Physics
Group Theory
math.MP
Abstract
We show that the associativity condition of the universal symmetric 2-algebraic 2-valued group defined by the Buchstaber polynomial admits several mutually equivalent interpretations from the viewpoints of the Chazy equation, Gauss-Manin connections, Dubrovin-Frobenius structures, and the quantum Yang-Baxter equation. These results place the universal 2-valued law in a unified framework linking geometry, algebraic topology, group theory, and mathematical physics.
Keywords
Cite
@article{arxiv.2604.26641,
title = {Two-Valued Groups, Chazy Equation, Dubrovin-Frobenius Structures, and QYBE},
author = {Victor Buchstaber and Mikhail Kornev and Vladimir Rubtsov},
journal= {arXiv preprint arXiv:2604.26641},
year = {2026}
}