1998/09/07 by Boris Shoikhet, Shoikhet, Boris
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Numerical methods for differential equations #Quantum Algebra (math.QA) #math.QA
paper · pdf · doi:10.48550/arxiv.math/9809037
24 pages, 2 Postscript figures, LaTeX2e
openalex publication_date 1998/09/07 · arxiv created 1999/01/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We integrate the Lifting cocycles Ψ2n+1,Ψ2n+3,Ψ2n+5,... ([Sh1], [Sh2]) on the Lie algebra \Difn of holomorphic differential operators on an n-dimensional complex vector space to the cocycles on the Lie algebra of holomorphic differential operators on a holomorphic line bundle λ on an n-dimensional complex manifold M in the sense of Gelfand-Fuks cohomology [GF] (more precisely, we integrate the cocycles on the sheaves of the Lie algebras of finite matrices over the corresponding associative algebras). The main result is the following explicit form of the Feigin-Tsygan theorem [FT1]: H^\bullet_\Lie(\gl^\fin_∞(\Difn);\C) = \wedge^\bullet(Ψ2n+1, Ψ2n+3,Ψ2n+5, ...).