Can I read Ordered tensor categories and representations of the Mackey Lie algebra of infinite matrices on EtoBox?

Ordered tensor categories and representations of the Mackey Lie algebra of infinite matrices by Chirvasitu, Alexandru; Penkov, Ivan is a scholarly article available to read on EtoBox.

What is Ordered tensor categories and representations of the Mackey Lie algebra of infinite matrices about?

We introduce (partially) ordered Grothendieck categories and apply results on their structure to the study of categories of representations of the Mackey Lie algebra of infinite matrices $\mathfrak{gl}^M\left(V,V_*\right)$. Here $\mathfrak{gl}^M\left(V,V_*\right)$ is the Lie algebra of endomorphisms of a nondegenerate pairing of countably infinite-dimensional vector spaces $V_*\otimes V\to\mathbb{K}$, where $\mathbb{K}$ is the base field. Tensor representations of $\mathfrak{gl}^M\left(V,V_*\right)$ are defined as arbitrary subquotients of finite direct sums of tensor products $(V^*)^{\otimes m}\otimes (V_*)^{\otimes n}\otimes V^{\otimes p}$ where $V^*$ denotes the algebraic dual of $V$. The category $\mathbb{T}^3_{\mathfrak{gl}^M\left(V,V_*\right)}$ which they comprise, extends a category $\mathbb{T}_{\mathfrak{gl}^M\left(V,V_*\right)}$ previously studied in [4, 12,17], and our main result is that $\mathbb{T}^3_{\mathfrak{gl}^M\left(V,V_*\right)}$ is a finite-length, Koszul self-dual, tensor category with a certain universal property that makes it into a "categorified algebra" defined by means of a handful of generators and relations. This result uses essentially the general prope

Author

Chirvasitu, Alexandru; Penkov, Ivan

Published

2015

Language

EN