Bosonic realization of toroidal Lie algebras of classical types

Details Bosonic realization of toroidal Lie algebras of classical types Bosonic realization of toroidal Lie algebras of classical types

2009-08-03

arxiv.org/abs/0908.0211v1

Proc. Amer. Math. Soc. 137 (2009), 3609-3618

Mathematics

Quantum Algebra

Scientific paper

Generalizing Feingold-Frenkel's construction we use Weyl bosonic fields to
construct toroidal Lie algebras of types $A_n, B_n$, $C_n$ and $D_n$ of level
$-1, -2, -1/2$ and -2 respectively. In particular, our construction also gives
new bosonic construction for the orthogonal Lie algebras in the cases of affine
Lie algebras.

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