24/11/2016

Palestrante: Daniel Levcovitz (ICMC-USP)

Título : On the isotropy group of a simple derivation.

Resumo: Let R = K[X1; : : : ;Xn] be a polynomial ring in n variables over a field K of charactersitic zero and d a K-derivation of R. Consider the isotropy group if d. In his doctoral thesis, Baltazar proved that if d is a simple Shamsuddin derivation of K[X1;X2], then its isotropy group is trivial. He also gave an example of a non-simple derivation whose isotropy group is infinite. Recently, Mendes and Pan generalized this result to an arbitrary derivation of K[X1;X2], proving that a derivation of K[X1;X2] is simple if, and only if, its isotropy group is trivial. In this talk, we prove that the isotropy group of a simple Shamsuddin derivation of the polynomial ring R = K[X1; : : : ;Xn] is trivial.

We also calculate other isotropy groups of (not necessarily simple) derivations of K[X1;X2] and prove that they are finite cyclic groups. These results are a joint work with Luciene Bertocello.