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

TL;DR

This paper explores the generalization of N=6 three-algebras to N=5, connecting anti-Lie triple systems with Lie superalgebras and demonstrating their relevance to N=5 superconformal theories in three dimensions.

Contribution

It introduces N=5 three-algebras linked to anti-Lie triple systems and basic Lie superalgebras, expanding the mathematical framework for superconformal theories.

Findings

Structure constants match between anti-Lie triple systems and N=5 theories

Generalization from N=6 to N=5 three-algebras established

Connection to basic Lie superalgebras of type II confirmed

Abstract

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.