Bosonic and fermionic representations of Lie algebra central extensions

Given any representation of an arbitrary Lie algebra g over a field K of characteristic 0, we construct representations of a central extension of g on bosonic and fermionic Fock space. The method gives an explicit formula for a (sometimes trivial) 2-cocycle in H-2(g; K). We illustrate these techniques with several concrete examples. (c) 2004 Elsevier Inc. All rights reserved.