Decomposition of the lattice vertex operator algebra V√2Al

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 V-root2Al 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 V-root2Al 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 V-root2Al as a direct sum of irreducible modules of W = L(c(1), 0) circle times L(c(2), 0) circle times(...)circle times L(c(l), 0) circle times Wl+1 (2l/(l + 3)), where c(i), i = 1,..., l, is given by the discrete series c(i) = 1 - 6/(i + 2)(i + 3), is also obtained. (C) 2004 Elsevier Inc. All rights reserved.