Extension of vertex operator algebra $V_{{\hat{H}}_4}(\ell ,0)$

Abstract

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.

28 pages

References in corpus (1)

• String interactions in gravitational wave backgrounds