Getzler, Ezra Cyclic homology and the Beilinson-Manin-Schechtman central extension. (English) Zbl 0692.17007 Proc. Am. Math. Soc. 104, No. 3, 729-734 (1988). Summary: The author constructs central extensions of the Lie algebra of differential operators on a one-dimensional affine variety over a field of characteristic zero, generalizing the Virasoro extension. The construction is an application of recent calculations of the Hochschild and cyclic homology of algebras of differential operators. Cited in 5 Documents MSC: 17B65 Infinite-dimensional Lie (super)algebras 17B56 Cohomology of Lie (super)algebras 14F40 de Rham cohomology and algebraic geometry 32C38 Sheaves of differential operators and their modules, \(D\)-modules 58J99 Partial differential equations on manifolds; differential operators Keywords:Hochschild homology; cyclic homology; central extensions; Lie algebra of differential operators Citations:Zbl 0645.17008 PDFBibTeX XMLCite \textit{E. Getzler}, Proc. Am. Math. Soc. 104, No. 3, 729--734 (1988; Zbl 0692.17007) Full Text: DOI