The second Lie algebra cohomology group and Weyl modules

John Brendan Sullivan

Vol. 86 (1980), No. 1, 321–326

DOI: 10.2140/pjm.1980.86.321

Abstract

The Lie algebra 1-cohomology of classical Lie algebras in characteristic p is nonzero at some modules. In fact, Hochschild showed that the restricted 1-cohomology is non-zero. Here I will systematically produce Weyl modules at which the (unrestricted) 2-cohomology is nonzero. This will provide examples of nonsplit abelian extensions of Lie algebras by Weyl modules in characteristic p, where the Lie algebras are the reductions modulo p of integral Chevalley forms of complex semisimple Lie algebras.

Mathematical Subject Classification 2000

Primary: 17B56

Secondary: 17B50, 20G10

Milestones

Received: 19 June 1978

Published: 1 January 1980