Abstract Crystals for Quantum Generalized Kac-Moody Algebras
  In this paper, we introduce the notion of abstract crystals for quantum generalized Kac-Moody algebras and study their fundamental properties. We then prove the crystal embedding theorem and give a characterization of the crystals $B(\infty)$ and $B(\la)$. 
Kyeonghoon Jeong, Seok-Jin Kang, Masaki Kashiwara and Dong-Uy Shin