2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/159649We revisit the third fundamental theorem of Lie (Lie III) for finite dimensional Lie algebras in the context of infinite dimensional matrices.This is a contribution to the Proc. of the Seventh International Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007, Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/Representation TheoryGroup TheoryAn Infinite Dimensional Approach to the Third Fundamental Theorem of Lietext