
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.
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