WITHDRAWN: Lifting formulas, Moyal product, and Feigin spectral sequence

Abstract: It is shown, that each Lifting cocycle

P s i_{2 n + 1}, P s i_{2 n + 3}, P s i_{2 n + 5}, . . .

([Sh1], [Sh2]) on the Lie algebra

D i f_{n}

of polynomial differential operators on an

n

-dimensional complex vector space is the sum of two cocycles, its even and odd part. We study in more details the first case

n = 1

. It is shown, that any nontrivial linear combination of two 3-cocycles on the Lie algebra

D i f_{1}

, arising from the 3-cocycle~

P s i_{3}

, is not cohomologous to zero, in a contradiction with the Feigin conjecture~[F]. The new conjecture on the cohomology

H^{d} o t_{L} i e (D i f_{1}; C)

is made.

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