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Let $k$ be a field of zero characteristic, and $R$ be a $k$-domain. Then  (i) The kernel of any triangular $R$-derivation of $R^{[n]}$ is non-rigid.  (ii) The kernel of any linear locally nilpotent derivation of $R^{[n]}$ isnon-rigid.

Rigidity of the kernel of a locally nilpotent derivation of a polynomial ring