Cyclic homology and the Beĭlinson-Manin-Schechtman central extension
HTML articles powered by AMS MathViewer
- by Ezra Getzler PDF
- Proc. Amer. Math. Soc. 104 (1988), 729-734 Request permission
Abstract:
We construct 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.References
- A. A. Beĭlinson, Yu. I. Manin, and V. V. Schechtman, Sheaves of the Virasoro and Neveu-Schwarz algebras, $K$-theory, arithmetic and geometry (Moscow, 1984–1986) Lecture Notes in Math., vol. 1289, Springer, Berlin, 1987, pp. 52–66. MR 923135, DOI 10.1007/BFb0078367 J. L. Block, Excision in cyclic homology of topological algebras, Harvard Univ. thesis, 1987.
- Jean-Luc Brylinski and Ezra Getzler, The homology of algebras of pseudodifferential symbols and the noncommutative residue, $K$-Theory 1 (1987), no. 4, 385–403. MR 920951, DOI 10.1007/BF00539624 A. Connes, Non-commutative differential geometry, Inst. Hautes Études Sci. Publ. Math. 62 (1985), 41-144.
- Charles Ehresmann and Paulette Libermann, Sur le problème d’équivalence des formes différentielles extérieures quadratiques, C. R. Acad. Sci. Paris 229 (1949), 697–698 (French). MR 32086
- G. Hochschild, Bertram Kostant, and Alex Rosenberg, Differential forms on regular affine algebras, Trans. Amer. Math. Soc. 102 (1962), 383–408. MR 142598, DOI 10.1090/S0002-9947-1962-0142598-8
- C. Kassel and J.-L. Loday, Extensions centrales d’algèbres de Lie, Ann. Inst. Fourier (Grenoble) 32 (1982), no. 4, 119–142 (1983) (French, with English summary). MR 694130, DOI 10.5802/aif.896 C. Kassel and C. Mitschi, Private communication.
- Jean-Louis Loday and Daniel Quillen, Cyclic homology and the Lie algebra homology of matrices, Comment. Math. Helv. 59 (1984), no. 4, 569–591. MR 780077, DOI 10.1007/BF02566367
- Edward Witten, Quantum field theory, Grassmannians, and algebraic curves, Comm. Math. Phys. 113 (1988), no. 4, 529–600. MR 923632, DOI 10.1007/BF01223238
- Mariusz Wodzicki, Cyclic homology of differential operators, Duke Math. J. 54 (1987), no. 2, 641–647. MR 899408, DOI 10.1215/S0012-7094-87-05426-3
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 104 (1988), 729-734
- MSC: Primary 17B35; Secondary 17B65, 19D55, 32C38, 58G07
- DOI: https://doi.org/10.1090/S0002-9939-1988-0936774-5
- MathSciNet review: 936774