Pensieve header: The double and meta-double of the 2D pencil; continued pensieve://2017-05/.

SetDirectory["C:\\drorbn\\AcademicPensieve\\2017-04"];
Once[Get["UEA`"]]

I hope to stick to G=(e^g) and to H=(e^h), where [g,e]=γ e and [h,f]=-η f.

$Basis={g,G,e,h,H,f}; $PBWRule=Thread[$Basis->Range@Length@$Basis];
B[g,e] = γ e; B[h,f] = -ηf;

With[{G=(Subscript[U, 1])[]+(Subscript[U, 1])[g]+(1/2)(Subscript[U, 1])[g,g]}, UB[G,(Subscript[U, 1])[e]]]