COHOMOLOGY OF TRUNCATED COINDUCED REPRESENTATIONS OF LIE ALGEBRAS OF POSITIVE CHARACTERISTIC

Abstract

The author proves that for any n-dimensional Lie algebra of characteristic p > 0 and any k, 0 ? k ? n, there exists a finite-dimensional module with nontrivial k-cohomology; the nontrivial cocycles of such modules become trivial under some finite-dimensional extension. He also obtains a criterion for the Lie algebra to be nilpotent in terms of irreducible modules with nontrivial cohomology. The proof of these 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.