Two-Valued Groups, Chazy Equation, Dubrovin-Frobenius Structures, and QYBE

TL;DR

This paper explores the deep connections between 2-valued groups, the Chazy equation, Frobenius structures, and the quantum Yang-Baxter equation, unifying various mathematical frameworks.

Contribution

It provides a unified interpretation of the associativity condition of universal symmetric 2-valued groups across multiple mathematical disciplines.

Findings

Multiple equivalent interpretations of associativity condition

Linking geometry, algebraic topology, and physics

Unified framework for 2-valued groups and related structures

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.