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Differential Forms and Lie Algebra Cohomology for Algebraic Linear Groups

In: Collected Papers

Author

Listed:
  • G. Hochschild
  • Bertram Kostant

    (Massachusetts Institute of Technology, Department of Mathematics)

Abstract

In the study of the rational cohomology theory of algebraic linear groups, the differential forms, constructed from the algebra of the rational representative functions on the group, play a major role in providing the link between the group cohomology and the Lie algebra cohomology [5]. Moreover, the cohomology of the differential forms has some significance as an algebraic geometric invariant. For instance, it follows from [5, Theorem 4.1] that, if R is the algebra of the rational representative functions on an irreducible algebraic linear group G over a field F of characteristic 0, the cohomology of the differential forms of R is trivial (if and) only if R is an ordinary polynomial algebra over F.

Suggested Citation

  • G. Hochschild & Bertram Kostant, 2009. "Differential Forms and Lie Algebra Cohomology for Algebraic Linear Groups," Springer Books, in: Anthony Joseph & Shrawan Kumar & Michèle Vergne (ed.), Collected Papers, pages 291-308, Springer.
    • Handle: RePEc:spr:sprchp:978-0-387-09583-7_15
    DOI: 10.1007/b94535_15
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