Algebra of Formal Vector Fields on the Line and Buchstaber's Conjecture

We consider the Lie algebra $L_1$ of formal vector fields on the line which vanish at the origin together with their first derivatives. V. M. Buchstaber and A. V. Shokurov showed that the universal enveloping algebra $U(L_1)$ is isomorphic to the Landweber–Novikov algebra $S$ tensored \with the reals. The cohomology $H^*(L_1)=H^*(U(L_1))$ was originally calculated by L. V. Goncharova. It follows from her computations that the multiplication in the cohomology $H^*(L_1)$ is trivial. Buchstaber conjectured that the cohomology $H^*(L_1)$ is generated with respect to nontrivial Massey products by one-dimensional cocycles. B. L. Feigin, D. B. Fuchs, and V. S. Retakh found a representation for additive generators of $H^*(L_1)$ in the desired form, but the Massey products indicated by them later proved to contain the zero element. In the present paper, we prove that $H^*(L_1)$ is recurrently generated with respect to nontrivial Massey products by two one-dimensional cocycles in $H^1(L_1)$.