Vertex operator representations for TKK algebras

It is known that, up to isomorphism, there are only one lattice S and one non-lattice semi-lattice S' in R-2. In [S. Tan, TKK algebras and vertex operator representations, J. Algebra 211 (1999) 298-342] we obtained a vertex operator representation for the baby-TKK algebra G(T(S')). The goal of the present paper is to study the TKK algebra G(T(S)), which includes the baby-TKK algebra as a subalgebra, and its vertex operator representations. As a by-product, we also obtain two representations for the baby-TKK algebra G(T(S')). One of the representations recovers the construction given in [S. Tan, TKK algebras and vertex operator representations, J. Algebra 211 (1999) 298-342]. (c) 2006 Elsevier Inc. All rights reserved.