Let $\mathfrak{ g}$ be a Borcherds-Bozec algebra, $U(\mathfrak{ g})$ be its universal enveloping algebra and $U_{ q}(\mathfrak{ g})$ be the corresponding quantum Borcherds-Bozec algebra. We show that the classical limit of $U_{ q}(\mathfrak{ g})$ is isomorphic to $U(\mathfrak{ g})$ as Hopf algebras. Thus $U_{ q}(\mathfrak{ g})$ can be regarded as a quantum deformation of $U(\mathfrak{ g})$. We also give explicit formulas for the commutation relations among the generators of $U_{ q}(\mathfrak{ g})$.
Categories: math.RT