From the braided to the usual Yang-Baxter relation

TL;DR

This paper modifies quantum monodromy matrices from coupled mKdV equations to satisfy the standard Yang-Baxter relation, establishing a link between braided and unbraided Yang-Baxter algebras.

Contribution

It introduces a method to convert braided quantum monodromy matrices into ones satisfying the usual Yang-Baxter relation, revealing a connection between different algebraic structures.

Findings

Modified monodromy matrices satisfy the usual Yang-Baxter relation.

Established a general connection between braided and unbraided Yang-Baxter algebras.

Analyzed the implications of this connection for integrable models.

Abstract

Quantum monodromy matrices coming from a theory of two coupled (m)KdV equations are modified in order to satisfy the usual Yang-Baxter relation. As a consequence, a general connection between braided and {\it unbraided} (usual) Yang-Baxter algebras is derived and also analysed.