In this paper, we develop the perfect basis theory for quantum Borcherds-Bozec algebras Uq( g) and their irreducible highest weight modules V(λ). We show that the lower perfect graph (resp. upper perfect graph) of every lower perfect basis (resp. upper perfect basis) of Uq⁻( g) (resp. V(λ)) is isomorphic to the crystal B(∞) (resp. B(λ)).
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Fan et al. (2024) studied this question.
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