On the conjecture of Kashuba and Mathieu about free Jordan algebras
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866911030478635008 |
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| author | Dotsenko, Vladimir Hentzel, Irvin Roy |
| author_facet | Dotsenko, Vladimir Hentzel, Irvin Roy |
| contents | Kashuba and Mathieu proposed a conjecture on vanishing of Lie algebra homology, implying a description of the $GL_d$-module structure of the free $d$-generated Jordan algebra. Their conjecture relies on a functorial version of the Tits--Kantor--Koecher construction that builds Lie algebras out of Jordan algebras. In this note, we summarize new intricate computational data concerning free Jordan algebras and explain why, despite a lot of overwhelmingly positive evidence, the conjecture of Kashuba and Mathieu is not true. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_00437 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the conjecture of Kashuba and Mathieu about free Jordan algebras Dotsenko, Vladimir Hentzel, Irvin Roy Rings and Algebras K-Theory and Homology Quantum Algebra Kashuba and Mathieu proposed a conjecture on vanishing of Lie algebra homology, implying a description of the $GL_d$-module structure of the free $d$-generated Jordan algebra. Their conjecture relies on a functorial version of the Tits--Kantor--Koecher construction that builds Lie algebras out of Jordan algebras. In this note, we summarize new intricate computational data concerning free Jordan algebras and explain why, despite a lot of overwhelmingly positive evidence, the conjecture of Kashuba and Mathieu is not true. |
| title | On the conjecture of Kashuba and Mathieu about free Jordan algebras |
| topic | Rings and Algebras K-Theory and Homology Quantum Algebra |
| url | https://arxiv.org/abs/2507.00437 |