Decomposition of the lattice vertex operator algebra V2Al

AbstractMotivated by the work of Dong et al. [Associative subalgebras of Griess algebra and related topics, in: J. Ferrar, K. Harada (Eds.), Proc. Conf. Monster and Lie Algebras, de Gruyter, Berlin, 1998], we study a decomposition of the lattice vertex operator algebra V2Al as a direct sum of irreducible modules of a certain tensor product of Virasoro vertex operator algebras and a parafermion algebra Wl+1(2l/(l+3)). We find that the vertex operator algebra V2Al contains a subalgebra isomorphic to a parafermion algebra Wl+1(2l/(l+3)) of central charge 2l/(l+3). A complete decomposition of the vertex operator algebra V2Al as a direct sum of irreducible modules of W=L(c1,0)⊗L(c2,0)⊗⋯⊗L(cl,0)⊗Wl+1(2l/(l+3)), where ci, i=1,…,l, is given by the discrete series ci=1−6/(i+2)(i+3), is also obtained