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00925njm 22002777a 4500 dc Cabrera-Casado, Yolanda author Draper-Fontanals, Cristina author Garvin-García, Antonio José author 2025-08-06 This work presents five explicit constructions of the exceptional Lie algebra e8, each associated with a semisimple subalgebra of maximal rank. The provided models are based on gradings by finite abelian groups, namely, Z4, Z5, Z6, Z2 3, and Z2 ×Z4. In all cases, the neutral component is a direct sum of special linear algebras, while the remaining homogeneous components are irreducible modules over it. Cabrera, Y., Draper, C. & Garvín, A. Linear models of the exceptional Lie algebra . Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 119, 108 (2025). https://doi.org/10.1007/s13398-025-01768-3 https://hdl.handle.net/10630/39939 10.1007/s13398-025-01768-3 Algebra multilineal Lie, Algebras de, excepcionales Matemáticas aplicadas Linear models of the exceptional Lie algebra e8