Differential Forms and Lie Algebra Cohomology for Algebraic Linear Groups

G. Hochschild and Bertram Kostant ()
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Bertram Kostant: Massachusetts Institute of Technology, Department of Mathematics

A chapter in Collected Papers, 2009, pp 291-308 from Springer

Abstract: 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.

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-387-09583-7_15

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DOI: 10.1007/b94535_15

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