Borcherds-Bozec algebras, root multiplicities and the Schofield construction
Abstract
Using the twisted denominator identity, we derive a closed form root multiplicity formula for all symmetrizable Borcherds-Bozec algebras and discuss its applications including the case of Monster Borcherds-Bozec algebra. In the second half of the paper, we provide the Schofield constuction of symmetric Borcherds-Bozec algebras.
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