In this paper, we develop the theory of abstract crystals for quantum Borcherds-Bozec algebras. Our construction is different from the one given by Bozec. We further prove the crystal embedding theorem and provide a characterization of ${ B}(\infty)$ and ${ B}(\lambda)$ as its application, where ${ B}(\infty)$ and ${ B}(\lambda)$ are the crystals of the negative half part of the quantum Borcherds-Bozec algebra $U_q(\mathfrak g)$ and its irreducible highest weight module $V(\lambda)$, respectively.
Categories: math.RT