Bosonic and Fermionic Representations of Lie Algebra Central Extensions

2004/05/29 by Michael Lau, Lau, Michael
Mathematics · Physics and Astronomy · #17B10 (Primary) 17B56 #17B65 #17B68 (Secondary) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Representation Theory (math.RT) #math-ph #math.MP #math.RT #msc:17B10 #msc:17B56 #msc:17B65 #msc:17B68

paper · pdf · doi:10.48550/arxiv.math/0405576

25 pages

arxiv created 2004/05/29 · arxiv updated 2009/12/01

Abstract

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 H²(L;k). We illustrate these techniques with several concrete examples.

Related

• Lie Algebras in Fock Space
• Bosonic and Fermionic Representations of Endomorphisms of Exterior Algebras
• Bosonic and fermionic representations of endomorphisms of exterior algebras
• Notes on Fock space
• Indecomposable representations and oscillator realizations of the exceptional Lie algebra G₂