We study Lie subalgebras L of the vector fields Vecc(A2) of affine 2-space A2 of constant divergence, and we classify those L which are isomorphic to the Lie algebra aff2 of the group Aff2(K) of affine transformations of A2. We then show that the following statements are equivalent:
(a) The Jacobian Conjecture holds in dimension 2;
(b) All Lie subalgebras L ⊂ Vecc(A2) isomorphic to aff2 are conjugate under Aut(A2);
(c) All Lie subalgebras L ⊂ Vecc(A2) isomorphic to aff2 are algebraic.
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