Given a simple finite-dimensional Lie algebra and an automorphism of finite order, one defines the notion twisted toroidal algebra. In this paper, we construct representations algebras from modules over affine lattice vertex algebras.

If A is a unital associative algebra and u is invertible in A, one can define an algebra A, called the u-isotope of A, which is equal to A as a vector space but has a new product x ·u y = xuy. This isotope A (u) is again unital and associative but with a shifted identity element u. More generally there are definitions of isotope for several other classes of unital nonassociative algebras, notab...

Rogers-Ramanujan type partition identities establish equalities between certain types of partitions with difference conditions and partitions whose generating functions is an infinite product. Since the 1980’s, many connections between representations of Lie algebras and RogersRamanujan type partition identities have emerged. Lepowsky and Wilson [6] were the first to establish this link by givi...

The author considers an elliptic analogue of the Knizhnik-Zamolodchikov equations – the consistent system of linear differential equations arising from the elliptic solution of the classical Yang-Baxter equation for the Lie algebra sl N. The solutions of this system are interpreted as traces of products of intertwining operators between certain representations of the affine Lie algebra sl N. A ...

The notion of a Weyl module, previously defined for the untwisted affine algebras, is extended here to the twisted affine algebras. We describe an identification of the Weyl modules for the twisted affine algebras with suitably chosen Weyl modules for the untwisted affine algebras. This identification allows us to use known results in the untwisted case to compute the dimensions and characters ...

We discuss the mutually opposite procedures of deformations and contractions of Lie algebras. Our main purpose is to illustrate the fact that, with appropriate combinations of both procedures, we obtain new Lie algebras. Firstly, we discuss low-dimensional Lie algebras, and these simple examples illustrate that, whereas for every contraction there exists a reverse deformation, the converse is n...

I gave two talks on some of my results on toroidal Lie algebras in the conference Functional Analysis VIII held in Dubrovnik, Croatia in June 2003. But these results have been submitted to research journals and will appear soon. So I decided to write an expository article on Toroidal Lie Algebras covering my results for the proceedings of Functional Analysis VIII. I will introduce the definitio...

In this contributed presentation, we discuss and compare the mutually opposite procedures of deformations and contractions of Lie algebras. We suggest that with appropriate combinations of both procedures one may construct new Lie algebras. We first discuss low-dimensional Lie algebras and illustrate thereby that whereas for every contraction there exists a reverse deformation, the converse is ...

Abstract Tensor hierarchy algebras are infinite-dimensional generalisations of Cartan-type Lie superalgebras. They not contragredient, exhibiting an asymmetry between positive and negative levels. These superalgebras have been a focus attention due to the fundamental rôle they play for extended geometry. In present paper, we examine tensor which super-extensions over-extended (often, hyperbolic...