On simplicity of vacuum modules

Details On simplicity of vacuum modules On simplicity of vacuum modules

2006-05-31

arxiv.org/abs/math-ph/0606002v2

Physics

Mathematical Physics

54 pages. 6/14/06: Corollary 9.1.5(ii) is replaced by a complete version and its proofis added

Scientific paper

We find necessary and sufficient conditions of irreducibility of vacuum
modules over affine Lie algebras and superalgebras. From this we derive
conditions of simplicity of minimal W-algebras. Moreover, in the case of
Virasoro and Neveu-Schwarz algebras we obtain explicit formulas for vacuum
determinants.

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