Algebras Satisfying Triality and S_4-symmetry

TL;DR

This paper reviews recent developments in non-associative Lie algebras that satisfy triality relations and exhibit S_4 symmetry, highlighting their algebraic structures and symmetries.

Contribution

It provides a comprehensive review of Lie algebras with triality relations and their connection to S_4 symmetry, emphasizing recent research progress.

Findings

Lie algebras satisfying triality relations are closely related to S_4 symmetry.

The paper summarizes recent advances in understanding these algebraic structures.

Connections between triality, Lie algebras, and symmetric group actions are elucidated.

Abstract

We give a review of recent works for non-associative algebras, especially Lie algebras satisfying the triality relation. They are also intimately related to S_4 (symmetric group of 4-objects) symmetry of the Lie algebras.