From Lie algebra crossed modules to tensor hierarchies

On Lie algebra crossed modules

The goal of this article is to construct a crossed module representing the cocycle 〈[, ], 〉 generating H(g; C) for a simple complex Lie algebra g.

Koszul Duality for modules over Lie algebra

Let G be a compact Lie group. Set Λ• = H∗(G) and S • = H(BG). The coefficients are in R or C. Suppose G acts on a reasonable space X. In the paper [GKM] Goresky, Kottwitz and MacPherson established a duality between the ordinary cohomology which is a module over Λ• and equivariant cohomology which is a module over S • . This duality is on the level of chains, not on the level of cohomology. The...

Vertex Operator Algebra Structure of Standard Affine Lie Algebra Modules

Modules of the toroidal Lie algebra $widehat{widehat{mathfrak{sl}}}_{2}$

‎Highest weight modules of the double affine Lie algebra $widehat{widehat{mathfrak{sl}}}_{2}$ are studied under a‎ ‎new triangular decomposition‎. ‎Singular vectors of Verma modules are‎ ‎determined using a similar condition with horizontal affine Lie‎ ‎subalgebras‎, ‎and highest weight modules are described under the‎ ‎condition $c_1>0$ and $c_2=0$.

Whittaker Modules for a Lie Algebra of Block Type

In this paper, we study Whittaker modules for a Lie algebras of Block type. We define Whittaker modules and under some conditions, obtain a one to one correspondence between the set of isomorphic classes of Whittaker modules over this algebra and the set of ideals of a polynomial ring, parallel to a result from the classical setting and the case of the Virasoro algebra.