Irreducible Integrable Modules for the full Toroidal Lie Algebras co-ordinated by Rational Quantum Torus

可积表示与由有理量子扭圈协调的扭形李代数

Integrable Representations for Toroidal Lie Algebras Co-ordinated by Rational Quantum Torus

本文研究了由有理量子扭圈协调的扭形李代数的不可约可积表示，完成其在中心作用平凡情况下的分类。

Classification of level zero irreducible integrable modules for twisted full toroidal Lie algebras

In this paper, we first construct the twisted full toroidal Lie algebra by an extension of a centreless Lie torus $LT$ which is a multiloop algebra twisted by several automorphisms of finite order and equipped with a particular grading. We then provide a complete classification of all the irreducible integrable modules with finite dimensional weight spaces for this twisted full toroidal Lie algebra having a non-trivial $LT$-action and where the centre of the underlying Lie algebra acts trivially.

Toroidal prefactorization algebras associated to holomorphic fibrations and a relationship to vertex algebras

Let $X$ be a complex manifold, $π: E \rightarrow X$ a locally trivial holomorphic fibration with fiber $F$, and $\mathfrak{g}$ a Lie algebra with an invariant symmetric form. We associate to this data a holomorphic prefactorization algebra $\mathcal{F}_{\mathfrak{g}, π}$ on $X$ in the formalism of Costello-Gwilliam. When $X=\mathbb{C}$, $\mathfrak{g}$ is simple, and $F$ is a smooth affine variety, we extract from $\mathcal{F}_{\mathfrak{g}, π}$ a vertex algebra which is a vacuum module for the universal central extension of the Lie algebra $\mathfrak{g} \otimes H^{0}(F, \mathcal{O})[z,z^{-1}]$…