Borcherds-Bozec algebras, root multiplicities and the Schofield construction
Seok-Jin Kang
TL;DR
This paper derives a closed-form root multiplicity formula for symmetrizable Borcherds-Bozec algebras using the twisted denominator identity and explores their Schofield construction.
Contribution
It introduces a new root multiplicity formula for Borcherds-Bozec algebras and provides a Schofield construction for symmetric cases.
Findings
Derived a closed-form root multiplicity formula.
Applied the formula to the Monster Borcherds-Bozec algebra.
Presented the Schofield construction for symmetric Borcherds-Bozec algebras.
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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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Advanced Algebra and Geometry