2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/225873We classify canonical metric 3-algebra structures on matrix algebras and find novel three-dimensional conformally invariant actions in N=4 projective superspace based on them. These can be viewed as Chern-Simons theories with special matter content and couplings. We explore the relations of these actions with the N=2 actions based on generalized 3-Lie algebras found earlier and relate them to the original Bagger-Lambert-Gustavsson action.1+18 pages, replaced with published versionHigh Energy Physics - Theorytext