Locally nilpotent derivations of affine domains
Any locally nilpotent derivation of an affine domain is equivalent to a restriction of a Jacobian type derivation of a polynomial ring.
The images of some simple derivations
In the paper, we study the relation between the images of polynomial derivations and their simplicity. We prove that the images of simple Shamsuddin derivations are not Mathieu-Zhao spaces. In addition, we also show that the images of some simple derivations in dimension three are not Mathieu-Zhao spaces. Thus, we conjecture that the images of simple derivations in dimension greater than one are not Mathieu-Zhao spaces. We also prove that locally nilpotent derivations are not simple in dimension greater than one.
Reductive group actions with one-dimensional quotient
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