Bosonic and Fermionic Representations of Lie Algebra Central Extensions

Details Bosonic and Fermionic Representations of Lie Algebra Central Extensions Bosonic and Fermionic Representations of Lie Algebra Central Extensions

2004-05-29

arxiv.org/abs/math/0405576v1

Mathematics

Representation Theory

25 pages

Scientific paper

Given any representation of an arbitrary Lie algebra L over a field k of
characteristic 0, we construct representations of L on bosonic and fermionic
Fock space. The method gives an explicit formula for a (sometimes trivial)
2-cocycle in H^2(L;k). We illustrate these techniques with several concrete
examples.

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