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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References
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© 2009 Springer-Verlag New York
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Hochschild, G., Kostant, B. (2009). Differential Forms and Lie Algebra Cohomology for Algebraic Linear Groups. In: Joseph, A., Kumar, S., Vergne, M. (eds) Collected Papers. Springer, New York, NY. https://doi.org/10.1007/b94535_15
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DOI: https://doi.org/10.1007/b94535_15
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