Algebra of formal vector fields on the line and Buchstaber's conjecture

Details Algebra of formal vector fields on the line and Buchstaber's conjecture Algebra of formal vector fields on the line and Buchstaber's conjecture

2008-07-03

arxiv.org/abs/0807.0653v1

Mathematics

Representation Theory

Scientific paper

Let L_1 denotes the Lie algebra of formal vector fields on the line which vanish at the origin together with their first derivatives. Buchstaber and Shokurov have shown that the universal enveloping algebra U(L_1) is isomorphic to the tensor product of the Landweber-Novikov algebra S in complex cobordism theory by reals. The cohomology H*(L_1) has trivial multiplication. Buchstaber conjectured that H*(L_1) is generated with respect to non-trivial Massey products by H^1(L_1). Feigin, Fuchs and Retakh found representation of H*(L_1) by trivial Massey products. In the present article we prove that H*(L_1) is generated with respect to non-trivial Massey products by two elements from H^1(L_1).

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