Quantum Braided Groups

TL;DR

This paper introduces quantum braided groups, a new algebraic structure generalizing quantum and braided groups, defined via solutions to the Yang-Baxter equation with specific conditions, supported by multiple examples.

Contribution

It defines quantum braided groups as a novel algebraic structure using pairs of Yang-Baxter solutions with additional constraints, expanding the framework of quantum algebra.

Findings

Defined quantum braided groups as a new algebraic structure.

Provided multiple examples illustrating these algebras.

Connected the structure to solutions of the Yang-Baxter equation.

Abstract

A new type of algebras that represent a generalization of both quantum groups and braided groups is defined. These algebras are given by a pair of solutions of the Yang--Baxter equation that satisfy some additional conditions. Several examples are presented.