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Cyclic homology and the Beĭlinson-Manin-Schechtman central extension


Author: Ezra Getzler
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
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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.


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  • [1] A. Beilinson, Yu. Manin and V. Schechtman, Sheaves of the Virasoro and Neveu-Schwartz algebras, $ K$-Theory, Arithmetic and Geometry, Lecture Notes in Math., vol. 1289, Springer-Verlag, Berlin, 1987. MR 923135 (89j:58039)
  • [2] J. L. Block, Excision in cyclic homology of topological algebras, Harvard Univ. thesis, 1987.
  • [3] J. L. Brylinski and E. Getzler, The homology of algebras of pseudo-differential symbols and the non-commutative residue, $ K$-Theory 1 (1987), 385-403. MR 920951 (89j:58135)
  • [4] A. Connes, Non-commutative differential geometry, Inst. Hautes Études Sci. Publ. Math. 62 (1985), 41-144.
  • [5] C. Ehresmann and P. Libermann, Sur le problème d'équivalence des formes diférentielles extérieures quadratiques, C. R. Acad. Sci. Paris 229 (1949), 697-698. MR 0032086 (11:251a)
  • [6] G. Hochschild, B. Kostant and A. Rosenberg, Differential forms on regular affine algebras, Trans. Amer. Math. Soc. 102 (1962), 383-408. MR 0142598 (26:167)
  • [7] C. Kassel and J. L. Loday, Extensions centrales d'algèbres de Lie, Ann. Inst. Fourier (Grenoble) 32 (1982), 119-142. MR 694130 (85g:17004)
  • [8] C. Kassel and C. Mitschi, Private communication.
  • [9] J. L. Loday and D. Quillen, Cyclic homology and the Lie algebra homology of matrices, Comment. Math. Helv. 59 (1984), 565-591. MR 780077 (86i:17003)
  • [10] E. Witten, Quantum field theory, grassmannians, and algebraic curves, Comm. Math. Phys. 133 (1988), 529-600. MR 923632 (88m:81127)
  • [11] M. Wodzicki, Cyclic homology of differential operators, Duke Math. J. 54 (1987), 641-648. MR 899408 (88k:32035)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0936774-5
Article copyright: © Copyright 1988 American Mathematical Society

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