Abstract crystals for quantum Borcherds-Bozec algebras


Abstract in English

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.

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