Over any field, the generalised Danielewski surfaces f(x)y = φ(x,z) have Makar-Limanov and Derksen invariants equal to K[x], their isomorphisms are classified, and a new family of stably isomorphic non-isomorphic surfaces gives cancellation counterexamples.
Gupta, On the cancellation problem for the affine space A3 in characteristic p , Invent
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On Generalised Danielewski Surfaces over fields of arbitrary characteristic
Over any field, the generalised Danielewski surfaces f(x)y = φ(x,z) have Makar-Limanov and Derksen invariants equal to K[x], their isomorphisms are classified, and a new family of stably isomorphic non-isomorphic surfaces gives cancellation counterexamples.