The nilpotent part M of the Borel of the "(Subscript[U, ϵ])[(Subscript[sl, 3])]" algebra illustrates a bug in the definition of the non-commutative multiplication **. Mathematica fails to simplify the highlighted expression during the evaluation, resulting in an infinite loop.

Implementing M

$k=3

DeclareAlgebra[M, Generators ->{X,Y,Z}, Centrals -> {}];
B[(Subscript[Y, M]),(Subscript[X, M])]=-ϵ M@Z;
B[(Subscript[Z, M]),(Subscript[X, M])]= -ϵ M[X,X,Y] ;
B[(Subscript[Z, M]),(Subscript[Y, M])]=-ϵ M[X,Y,Y];

( ϵ (Subscript[Y, M]))**M[X,Y,Y]

M[Y]**M[X,Y,Y]

(#1**M[Y,Y]&)[-ϵ M[Z]]

(#1**M[Y,Y]&)[M[X,Y]]

ϵ M[Z]**M[Y,Y]

0*(qq=7)

qq

SetAttributes[MM,HoldRest]; MM[0,_]=0; MM[a_,x_]:=a x;

MM[0,qq=8]

qq

MM[3,4]

MM[ϵ,ϵ]

ϵ

MM[(ϵ^2),qq=9]

qq