J. Lepowsky and R. L. Wilson initiated the approach to combinatorial Rogers-Ramanujan type identities via the vertex operator constructions of representations of affine Lie algebras. In a joint work with Arne Meurman this approach is developed further in the framework of vertex operator algebras. The main ingredients of that construction are defining relations for standard modules and relations...

We construct certain integral structures for the cores of reduced tame extended affine Lie algebras rank at least 2. One main tools to achieve this is a generalization Chevalley automorphisms in context algebras. As an application, groups type associated adjoint representation are defined over arbitrary fields.

Using n finite order automorphisms on a simple complex Lie algebra we construct twisted n-toroidal Lie algebras. Thus obtaining Lie algebras wich have a rootspace decomposition. For the case n = 2 we list certain simple Lie algebras and their automorphisms, which produce twisted 2-toroidal algebras. In this way we obtain Lie algebras that are related to all Extended Affine Root Systems of K. Sa...

An important theorem in the theory of infinite dimensional Lie algebras states that any affine Kac-Moody algebra can be realized (that is to say constructed explicitly) using loop algebras. In this paper, we consider the corresponding problem for a class of Lie algebras called extended affine Lie algebras (EALAs) that generalize affine algebras. EALAs occur in families that are constructed from...

We investigate a class of Lie algebras called quasi-simple Lie algebras. These are generalizations of semi-simple, reductive, and affine Kac-Moody Lie algebras. A quasi-simple Lie algebra which has an irreducible root system is said to be irreducible and we note that this class of algebras have been under intensive investigation in recent years. They have also been called extended affine Lie al...

We use a fermionic extension of the bosonic module to obtain a class of B(0, N)-graded Lie superalgebras with nontrivial central extensions. 0 Introduction B(M − 1, N)-graded Lie superalgebras were first investigated and classified up to central extension by Benkart-Elduque (see also Garcia-Neher’s work in [GN]). Those root graded Lie superalgebras are a super-analog of root graded Lie algebras...

In finite-dimensional simple Lie algebras and affine Kac-Moody algebras, Chevalley involutions are crucial ingredients of the modular theory. Towards establishing theory for extended we investigate existence “Chevalley involutions” tori algebras. We first discuss how to lift a involution from centerless core which is characterized be torus then entire algebra. prove by type-dependent argument t...