Special Freudenthal-Kantor triple systems and Lie algebras with dicyclic symmetry

TL;DR

This paper explores Lie algebras with dicyclic symmetry, revealing their connections to graded Lie algebras, J-ternary algebras, and Freudenthal-Kantor triple systems, thus advancing understanding of their structure and symmetries.

Contribution

It introduces special Freudenthal-Kantor triple systems linked to Lie algebras with dicyclic symmetry and explores their relationships with graded Lie algebras and J-ternary algebras.

Findings

Identifies connections between Lie algebras with dicyclic automorphisms and BC1-graded Lie algebras.

Establishes relationships with J-ternary algebras.

Links to Freudenthal-Kantor triple systems.

Abstract

Lie algebras endowed with an action by automorphisms of the dicyclic group of degree 3 are considered. The close connections of these algebras with Lie algebras graded over the nonreduced root system BC1, with J-ternary algebras and with Freudenthal-Kantor triple systems are explored.