Bachar Alhajjar

We investigate filtrations corresponding to degree functions induced by locally nilpotent derivations, and we present a class of invariant sub-algebras induced by means of locally nilpotent derivations. We introduce semi-rigid domains, that is, domains for which every non-zero locally nilpotent derivation gives rise to the same filtration, and we discus the correspondence between finitely generated semi-rigid domains and reduced, irreducible affine varieties that admit a unique special $\mathbb{A}^1$-fibration.