Article

On the non-existence of sympathetic Lie algebras with dimension less than 25

Details

Citation

Garcia Pulido AL & Salgado G (2023) On the non-existence of sympathetic Lie algebras with dimension less than 25. Journal of Algebra and Its Applications. https://doi.org/10.1142/S0219498825501221

Abstract
In this article we investigate the question of the lowest possible dimension that a sympathetic Lie algebra g can attain, when its Levi subalgebra gL is simple. We establish the structure of the nilradical of a perfect Lie algebra g, as a gL-module, and determine the possible Lie algebra structures that one such g admits. We prove that, as a gL-module, the nilradical must decompose into at least 4 simple modules. We explicitly calculate the semisimple derivations of a perfect Lie algebra g with Levi sub-algebra gL=sl2(C) and give necessary conditions for g to be a sympathetic Lie algebra in terms of these semisimple derivations. We show that there is no sympathetic Lie algebra of dimension lower than 15, independently of the nilradical’s decomposition. If the nilradical has 4 simple modules, we show that a sympathetic Lie algebra has dimension greater or equal than 25.

Keywords
Sympathetic Lie algebras; equivariant maps; inner derivations

Journal
Journal of Algebra and Its Applications

StatusEarly Online
FundersEngineering and Physical Sciences Research Council and Consejo Nacional de Ciencia y Tecnologia-Mexico
Publication date online08/12/2023
Date accepted by journal27/09/2023
URLhttp://hdl.handle.net/1893/35815
ISSN0219-4988
eISSN1793-6829

People (1)

Dr Ana Lucia Garcia Pulido

Dr Ana Lucia Garcia Pulido

Lect in Pure Math/Mathematical Mod, Mathematics