Year: 1998
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Shoikhet, Boris
Institution: Independent University of Moscow
Language: English
Topic: Advanced Topics in Algebra
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1607827271