Four bases for the Onsager Lie algebra related by a ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$ action

Jae-Ho Lee

The Onsager Lie algebra $O$ is an infinite-dimensional Lie algebra defined by generators $A$, $B$ and relations $[A,[A,[A,B]]]=4[A,B]$ and $[B,[B,[B,A]]]=4[B,A]$. Using…