Extension of vertex operator algebra $V_{\hat{H}_{4}}(\ell,0)$

Details Extension of vertex operator algebra $V_{\hat{H}_{4}}(\ell,0)$ Extension of vertex operator algebra $V_{\hat{H}_{4}}(\ell,0)$

2011-04-21

arxiv.org/abs/1104.4232v1

Mathematics

Quantum Algebra

28 pages

Scientific paper

We classify the irreducible restricted modules for the affine Nappi-Witten Lie algebra $\hat{H}_{4}$ with some natural conditions. It turns out the representation theory of $\hat{H}_{4}$ is quite different from the theory of representations of Heisenberg algebras. We also study the extension of the vertex operator algebra $V_{\hat{H}_{4}}(\ell,0)$ by the even lattice $L$. We give the structure of the extension $V_{\hat{H}_{4}}(\ell,0)\otimes \C[L]$ and its irreducible modules via irreducible representations of $V_{\hat{H}_{4}}(\ell,0)$ viewed as a vertex algebra.

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