Narrow Results

An explicit construction of indecomposable modules for the twisted Heisenberg–Virasoro algebra and representations for the full toroidal Lie algebras are given.

The authors construct a Wakimoto type realization of toroidal 𝔰𝔩_n+1. The representation constructed in this paper utilizes non-commuting differential operators acting on the tensor product of two polynomial rings in infinitely many commuting variables.

We construct a level -1/2 vertex representation of the quantum $N$-toroidal algebra of type $C_n$, which is a natural generalization of the usual quantum toroidal algebra. The construction also provides a vertex representation of the quantum toroidal algebra for type $C_n$ as a by-product.

This paper reviews some results on toroidal vertex algebras. In particular, the toroidal vertex algebras and their (twisted) modules by using multi-variables are reviewed, and simple toroidal vertex algebras and their irreducible modules are discussed. Some module categories for toroidal Lie algebras are studied by using formal variable techniques.