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- W2762409991 abstract "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 $V_*otimes Vto mathbb{K}$ 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 $tinmathbb{Z}_{geq 0}$." @default.
- W2762409991 created "2017-10-20" @default.
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- W2762409991 date "2017-10-03" @default.
- W2762409991 modified "2023-10-01" @default.
- W2762409991 title "Representation categories of Mackey Lie algebras as universal monoidal categories" @default.
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