A Koszul category of representations of finitary Lie algebras

Details A Koszul category of representations of finitary Lie algebras A Koszul category of representations of finitary Lie algebras

2011-05-17

arxiv.org/abs/1105.3407v1

Mathematics

Representation Theory

22 pages

Scientific paper

We find for each simple finitary Lie algebra $\mathfrak{g}$ a category $\mathbb{T}_\mathfrak{g}$ of integrable modules in which the tensor product of copies of the natural and conatural modules are injective. The objects in $\mathbb{T}_\mathfrak{g}$ can be defined as the finite length absolute weight modules, where by absolute weight module we mean a module which is a weight module for every splitting Cartan subalgebra of $\mathfrak{g}$. The category $\mathbb{T}_\mathfrak{g}$ is Koszul in the sense that it is antiequivalent to the category of locally unitary finite-dimensional modules over a certain direct limit of finite-dimensional Koszul algebras. We describe these finite-dimensional algebras explicitly. We also prove an equivalence of the categories $\mathbb{T}_{o(\infty)}$ and $\mathbb{T}_{sp(\infty)}$ corresponding respectively to the orthogonal and symplectic finitary Lie algebras $o(\infty)$, $sp(\infty)$.

Affiliated with

Also associated with

No associations

Rating

A Koszul category of representations of finitary Lie algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A Koszul category of representations of finitary Lie algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Koszul category of representations of finitary Lie algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-727868