Abstract
The cohomology of restricted Lie algebras was first defined by Hochschild in 1954, cf.[11]. It was however only recently that one could get more precise information about these cohomology groups in non-trivial cases. The most fascinating result is still the theorem (proved by Friedlander and Parshall) that for large p the cohomology ring of the Lie algebra of a reductive algebraic group is the ring of regular functions on the nilpotent cone in this Lie algebra. It is the purpose of this article to give a survey of recent developments in this theory.
Throughout this paper let k be an algebraically closed field with char(k)=p≠0.
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Jantzen, J.C. (1987). Restricted lie algebra cohomology. In: Cohen, A.M., Hesselink, W.H., van der Kallen, W.L.J., Strooker, J.R. (eds) Algebraic Groups Utrecht 1986. Lecture Notes in Mathematics, vol 1271. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0079234
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DOI: https://doi.org/10.1007/BFb0079234
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