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arXiv · 2507.17854

The structure of non-Fricke Monstrous Lie algebras

Daniel Tan
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Abstract

We consider Borcherds algebras with no real roots and the property that all zeroes in the Borcherds Cartan matrix occur in a single diagonal zero block. It follows that all other entries of the matrix are negative. We give a structure theorem for these Borcherds algebras, decomposing them into free, Heisenberg and abelian subalgebras. We show that a class of such Borcherds algebras are the Monstrous Lie algebras associated to non-Fricke elements of the Monster finite simple group. This new perspective on their structure gives an efficient method to compute their twisted denominator formulas.

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Daniel Tan. 2025-07-23. The structure of non-Fricke Monstrous Lie algebras. https://arxiv.org/abs/2507.17854

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