Malcev sl2-algebras

López Solís V. · Journal of Algebra and its Applications (2025) · DOI: 10.1142/s0219498826502737

Resumen

Recently, López Solís [On a problem by Nathan Jacobson for Malcev algebras, preprint (2025), arXiv:2106.01155] solved a problem for a certain class H of Malcev algebras, which is an analog of an old problem posed by Jacobson [7] for alternative algebras. Inspired by Grishkov and Shestakov [Alternative M2-algebras and Γ-algebras, São Paulo J. Math. Sci. 18(2) (2024) 696–709], here we give another description of Malcev sl2-algebras in H via a simple super-anticommutative superalgebra g(3, 2) and an auxiliar Z2-graded algebra Γ. It occurs that the category of Malcev sl2-algebras in H is isomorphic to the category of Γ-algebras.

Instituciones: Universidad Nacional de Barranca