Twisted tensor products of quantum affine vertex algebras and coproducts

Let g be a symmetrizable Kac-Moody Lie algebra, and let Vĝ,^, Lĝ,^ be the quantum affine vertex algebras constructed in [11]. For any complex numbers and ', we present an -adic quantum vertex algebra homomorphism Δ from Vĝ,+' to the twisted tensor product -adic quantum vertex algebra Vĝ,^⊗ Vĝ,'. In addition, if both and ' are positive integers, we show that Δ induces an -adic quantum vertex algebra homomorphism from Lĝ,+' to the twisted tensor product -adic quantum vertex algebra Lĝ,^⊗ Lĝ,'. Moreover, we prove the coassociativity of Δ.