Locally extended affine Lie algebras were introduced by Morita and Yoshii in [J. Algebra 301(1) (2006), 59-81] as a natural generalization of extended affine Lie algebras. After that, various generalizations of these Lie algebras have been investigated by others. It is known that a locally extended affine Lie algebra can be recovered from its centerless core, i.e., the ideal generated by weight...

locally extended affine lie algebras were introduced by morita and yoshii in [j. algebra 301(1) (2006), 59-81] as a natural generalization of extended affine lie algebras. after that, various generalizations of these lie algebras have been investigated by others. it is known that a locally extended affine lie algebra can be recovered from its centerless core, i.e., the ideal generated by weight...

We show that the representation theory for the toroidal extended affine Lie algebra is controlled by a VOA which is a tensor product of four VOAs: a sub-VOA V + Hyp of a hyperbolic lattice VOA, affine ˙ g and sl N VOAs and a Virasoro VOA. A tensor product of irre-ducible modules for these VOAs admits the structure of an irreducible module for the toroidal extended affine Lie algebra. We also sh...

We use fermionic representations to obtain a class of BC N -graded Lie algebras coordinatized by quantum tori with nontrivial central extensions. 0 Introduction Lie algebras graded by the reduced finite root systems were first introduced by Berman-Moody [BM] in order to understand the generalized intersection matrix algebras of Slodowy. [BM] classified Lie algebras graded by the root systems of...

We develop general results on centroids of Lie algebras and apply them to determine the centroid of extended affine Lie algebras, loop-like and Kac-Moody Lie algebras, and Lie algebras graded by finite root systems.

We obtain Drinfeld second realization of the quantum affine superalgebras associated with the affine Lie superalgebra D(1)(2, 1;x). Our results are analogous to those obtained by Beck for the quantum affine algebras. Beck’s analysis uses heavily the (extended) affine Weyl groups of the affine Lie algebras. In our approach the structures are based on a Weyl groupoid. Preprint numbers: MIT-CTP 38...

Iterated loop algebras are by definition obtained by repeatedly applying the loop construction, familiar from the theory of affine Kac-Moody Lie algebras, to a given base algebra. Our interest in this iterated construction is motivated by its use in the realization of extended affine Lie algebras, but the construction also appears naturally in the study of other classes of algebras. This paper ...