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Differential Forms on Regular Affine Algebras

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Abstract

The formal apparatus of the algebra of differential forms appears as a rather special amalgam of multilinear and homological algebra, which has not been satisfactorily absorbed in the general theory of derived functors. It is our main purpose here to identify the exterior algebra of differential forms as a certain canonical graded algebra based on the Tor functor and to obtain the cohomology of differential forms from the Ext functor of a universal algebra of differential operators similar to the universal enveloping algebra of a Lie algebra.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

    G. Hochschild, Bertram Kostant & Alex Rosenberg

Authors
  1. G. Hochschild
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  2. Bertram Kostant
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  3. Alex Rosenberg
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Corresponding author

Correspondence to Bertram Kostant .

Editor information

Editors and Affiliations

  1. Fac. Mathematics & Computer Science, Weizmann Institute of Science, Rehovot, 76100, Israel

    Anthony Joseph

  2. Dept. Mathematics, University of North Carolina, Phillips Hall, Chapel Hill, 27599-3250, U.S.A.

    Shrawan Kumar

  3. Centre de Mathématiques, Ecole Polytechnique, Palaiseau Cedex, 91128, France

    Michèle Vergne

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© 2009 Springer-Verlag New York

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Hochschild, G., Kostant, B., Rosenberg, A. (2009). Differential Forms on Regular Affine Algebras. In: Joseph, A., Kumar, S., Vergne, M. (eds) Collected Papers. Springer, New York, NY. https://doi.org/10.1007/b94535_14

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