The structure of non-Fricke Monstrous Lie algebras
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909703126122496 |
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| author | Tan, Daniel |
| author_facet | Tan, Daniel |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_17854 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The structure of non-Fricke Monstrous Lie algebras Tan, Daniel Representation Theory 17B65, 17B69 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. |
| title | The structure of non-Fricke Monstrous Lie algebras |
| topic | Representation Theory 17B65, 17B69 |
| url | https://arxiv.org/abs/2507.17854 |