2025/03/20 by Vladimir Dotsenko, Dotsenko, Vladimir · 1 citation
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Topics in Algebra #FOS: Mathematics #K-Theory and Homology (math.KT) #Quantum Algebra (math.QA) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2503.16074
openalex publication_date 2025/03/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02
Kashuba and Mathieu proposed a conjecture on vanishing of some components of the homology of certain Lie algebras, implying a description of the GLd-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. Recently, Shang used a functorial construction of Allison, Benkart and Gao that builds Lie algebras out of alternative algebras to propose another conjecture on vanishing of some components of the homology of certain Lie algebras, implying a description of the GLd-module structure of the free d-generated alternative algebra. In this note, we explain why the conjecture of Shang is not true.