Vol. 86, No. 1, 1980

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The second Lie algebra cohomology group and Weyl modules

John Brendan Sullivan

Vol. 86 (1980), No. 1, 321–326

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
Received: 19 June 1978
Published: 1 January 1980
John Brendan Sullivan