Vol. 83, No. 1, 1979

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On the low-dimensional cohomology of some infinite-dimensional simple Lie algebras

Stephen Berman

Vol. 83 (1979), No. 1, 27–36
Abstract

The two dimensional cohomology, with values in the base field K of characteristic 0, of a simple Lie algebra attached to any non-Euclidean indecomposable Cartan matrix is computed. We find that dim(H2(,K)) equals the nullity of the Cartan matrix which defines . We also show that there is an invariant 3-cocycle of if and only if the matrix defining is symmetrizable. This yields cohomological interpretations for all the known isomorphism class invariants of these algebras.

Mathematical Subject Classification 2000
Primary: 17B56
Secondary: 17B65
Milestones
Received: 31 July 1978
Revised: 2 January 1979
Published: 1 July 1979
Authors
Stephen Berman
University of Saskatchewan
Saskatoon SK
Canada