Isotropy group of an LND of the polynomial algebra in three variables

The talk is based on a joint work with Nikhilesh Dasgupta.

In the talk we will discuss some topics concerning locally nilpotent derivations of the algebra of polynomials in three variables. An important characteristic of an LND is its rank, that is, 3 minus the maximum number of variables that are contained in the kernel. Examples of non-triangulazible LND of rank 2 and LND of rank 3 will be given. The main object to be considered is a group of automorphisms commuting with a given LND (isotropy group). We will introduce a structure of the semi-direct product of two subgroups on this group. For triangulazible LNDs it will be calculated explicitly. Also we will discuss how this theory can be used to construct new examples of LNDs of rank 3.