Recoding Lie algebraic subshifts

We study internal Lie algebras in the category of subshifts on a fixed group – or algebraic for short. We show that if acting is virtually polycyclic and underlying vector space has dense homoclinic points, such can be recoded to have cellwise bracket. On other hand there exist (on any finitely-generated non-torsion group) with operations whose bracket cannot cellwise. also one-dimensional full shifts support infinitely many compatible brackets even up automorphisms shift, we state classification problem brackets. style='text-indent:20px;'>From attempts generalize these results groups, following questions arise: Does every f.g. admit linear cellular automaton infinite order? Which groups abelian not generated by finitely orbits? For first question, Grigorchuk admits CA, second lamplighter shifts.