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Differential Forms and Lie Algebra Cohomology for Algebraic Linear Groups

  • G. Hochschild
  • Bertram Kostant
Chapter

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.

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Copyright information

© Springer-Verlag New York 2009

Authors and Affiliations

  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

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