PlanetPhysics/Quantum Algebra

A quantum algebra over a field $$k$$ is defined as a triple $$(A, \rho, s)$$ where $$(A, \rho)$$ is a Yang-Baxter algebra over the field $$k$$ and $$s: A \to A^{op}$$ is an algebra isomorphism, subject to the following two axioms:


 * 1) (QA.1) $$\rho^{-1} = (s \otimes 1_A)(\rho)$$
 * 2) (QA.2) $$\rho = (s \otimes s)(\rho)$$

Note also that(QA.1) and(QA.2) imply(QA.3):

(QA.3) $$\rho^{-1} = (1_A \otimes s^{-1})(\rho)$$.

Remark Quasitriangular Hopf algebras are a basic source of quantum algebras.