arXiv:math/9810162math.QA
Lifting formulas, Moyal product, and Feigin spectral sequence
Abstract
It is shown, that each Lifting cocycle $Ψ_{2n+1},Ψ_{2n+3},Ψ_{2n+5},...$ ([Sh1], [Sh2]) on the Lie algebra $\Dif_n$ 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 $\Dif_1$, arising from the 3-cocycle~$Ψ_3$, is not cohomologous to zero, in a contradiction with the Feigin conjecture~[F]. The new conjecture on the cohomology $H^\ndot_\Lie(\Dif_1;\C)$ is made.
Previous versions such as https://arxiv.org/abs/math/9810162v1 clearly link to the latest withdrawn version, with text in red and bold at the top. Researchers accustomed to the arxiv don't miss it. Peer reviews don't catch some important mistakes. It does not guarantee much by…
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I make no claim to peer reviewed journals being better, I simply noted that the linked article asserted that two thirds of arXiv STEM preprints are latter submitted to such journals. > Previous versions such as https://arxiv.org/abs/math/9810162v1 clearly link to the latest…
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