Decomposition of the lattice vertex operator algebra

Motivated 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 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 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 as a direct sum of irreducible modules of , where ci, i=1,…,l, is given by the discrete series ci=1−6/(i+2)(i+3), is also obtained.