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Cyclic homology and the Beilinson-Manin-Schechtman central extension. (English) Zbl 0692.17007

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.

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

Citations:

Zbl 0645.17008
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