Decomposition of the lattice vertex operator algebra [formula omitted

Abstract

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 2 A l as a direct sum of irreducible modules of a certain tensor product of Virasoro vertex operator algebras and a parafermion algebra W l+1 (2 l/( l+3)). We find that the vertex operator algebra V 2 A l contains a subalgebra isomorphic to a parafermion algebra W l+1 (2 l/( l+3)) of central charge 2 l/( l+3). A complete decomposition of the vertex operator algebra V 2 A l as a direct sum of irreducible modules of W=L(c 1,0)⊗L(c 2,0)⊗⋯⊗L(c l,0)⊗W l+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.