Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Representation categories of Mackey Lie algebras as universal monoidal
  categories   Let $\mathbb{K}$ be an algebraically closed field of characteristic $0$. We
study a monoidal category $\mathbb{T}_\alpha$ which is universal among all
symmetric $\mathbb{K}$-linear monoidal categories generated by two objects $A$
and $B$ such that $A$ has a, possibly transfinite, filtration. We construct
$\mathbb{T}_\alpha$ as a category of representations of the Lie algebra
$\mathfrak{gl}^M(V_*,V)$ consisting of endomorphisms of a fixed diagonalizable
pairing $V_*\otimes V\to \mathbb{K}$ of vector spaces $V_*$ and $V$ of
dimension $\alpha$. Here $\alpha$ is an arbitrary cardinal number. We describe
explicitly the simple and the injective objects of $\mathbb{T}_\alpha$ and
prove that the category $\mathbb{T}_\alpha$ is Koszul. We pay special attention
to the case where the filtration on $A$ is finite. In this case
$\alpha=\aleph_t$ for $t\in\mathbb{Z}_{\geq 0}$.

22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
19
The categories of this paper are: eess