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Differential Forms on Regular Affine Algebras

In: Collected Papers

Author

Listed:
  • G. Hochschild

    (Massachusetts Institute of Technology, Department of Mathematics)

  • Bertram Kostant

    (Massachusetts Institute of Technology, Department of Mathematics)

  • Alex Rosenberg

    (Massachusetts Institute of Technology, Department of Mathematics)

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.

Suggested Citation

  • G. Hochschild & Bertram Kostant & Alex Rosenberg, 2009. "Differential Forms on Regular Affine Algebras," Springer Books, in: Anthony Joseph & Shrawan Kumar & Michèle Vergne (ed.), Collected Papers, pages 265-290, Springer.
    • Handle: RePEc:spr:sprchp:978-0-387-09583-7_14
    DOI: 10.1007/b94535_14
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