Abstract crystals for quantum Borcherds-Bozec algebras

Abstract

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.

31 pages