We discuss a generalization of N = 6 three-algebras to N = 5 three-algebras in connection to anti-Lie triple systems and basic Lie superalgebras of type II. We then show that the structure constants defined in anti-Lie triple systems agree with those of N = 5 superconformal theories in three dimensions.
Our work is supported by IISN -Belgium (conventions 4.4511.06 and 4.4514.08), by the Belgian Federal Science Policy Office through the Interuniversity Attraction Pole P6/11.