Classical limit of quantum Borcherds-Bozec algebras

Abstract

Let g be a Borcherds-Bozec algebra, U(g) be its universal enveloping algebra and Uq(g) be the corresponding quantum Borcherds-Bozec algebra. We show that the classical limit of Uq(g) is isomorphic to U(g) as Hopf algebras. Thus, Uq(g) can be regarded as a quantum deformation of U(g). We also provide explicit formulas for the commutation relations among the generators of Uq(g).