Realization for tensor products of Leavitt path algebras of hypergraphs

For two given hypergraphs, we construct an augmentation hypergraph. We establish an algebra homomorphism from the Leavitt path algebra of the augmentation hypergraph to the tensor product of the corresponding Leavitt path algebras of the two given hypergraphs. And we apply the homomorphism to certain weighted Leavitt path algebras of weighted graphs. We find a sufficient condition on weighted graphs such that one realizes the weighted Leavitt path algebras of the augmentation for weighted graphs as the tensor product of the weighted Leavitt path algebras.