N=5 three-algebras and 5-graded Lie superalgebras

Understand

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.