COHOMOLOGY OF TRUNCATED COINDUCED REPRESENTATIONS OF LIE-ALGEBRAS OF POSITIVE CHARACTERISTIC

The author proves that for any n-dimensional Lie algebra of characteristic p > 0 and any k, 0 ʎ k ʎ; n, there exists a finite-dimensional module with nontrivialk-cohomology; the nontrivial cocycles of such modules become trivial under somefinite-dimensional extension. He also obtains a criterion for the Lie algebra to benilpotent in terms of irreducible modules with nontrivial cohomology. The proof ofthese facts is based on a generalization of Shapiro's lemma. The truncated induced and coinduced representations are shown to be the same thing.Bibliography: 22 titles. © 1990 American Mathematical Society.