The notion of automorphic correction of a Lie algebra was originated from Borcherds's work on Monster Lie algebras. In this talk we consider rank two symmetric hyperbolic Kac-Moody algebras H(a) and their automorphic correction in terms of Hilbert modular forms. We associate a family of H(a)'s to the quadratic field Q(\sqrt p) for each odd prime p and show that there exists a chain of embeddings in each family. When p=5, 13, 17, we show that the first H(a) in each family is contained in a generalized Kac-Moody superalgebra whose denominator function is a Hilbert modular form given by a Borcherds product.

This is a joint work with Henry Kim.