On Shamsuddin derivations and the isotropy groups

Abstract

In the paper, we give an affirmative answer to the conjecture in [2]. We prove that a Shamsuddin derivation D is simple if and only if Aut(K[x, y 1 , . . . , y n ]) D = {id}. In addition, we calculate the isotropy groups of some Shamsuddin derivations of K[x, y 1 , . . . , y r ].

The images of some simple derivations

“…γ s = 0 has no positive integral solution, then the conclusion follows from Lemma 2.1 and Theorem 3.2 in [9]. Otherwise, we can assume that s i=1 |m (u)…”