Cohomology Theorems for Borel-Like Solvable Lie Algebras in Arbitrary Characteristic

This paper develops some techniques for the study of derivation algebras and cohomology groups of Lie algebras. We are especially concerned with solvable algebras over arbitrary fields with structural properties like those of the Borel subalgebras of complex semi-simple Lie algebras. In particular, these algebras are semi-direct sums of nilpotent ideals and abelian subalgebras which act on the ideals in a semi-simple fashion. We make strong use, in our discussion, of a cohomology theorem of Hochschild-Serre. This result is stated herein (§ 2) in a modified form which allows us to omit the original hypothesis that the base field have characteristic 0.

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