论文标题
对于可数维的空间V的GL（V）的拓扑张量表示
Topological tensor representations of gl(V) for a space V of countable dimension
论文作者
论文摘要
Lie代数$ gl（v）$是可计数维复合体矢量空间$ v $的所有内型的谎言代数。我们定义了lie代数$ gl（v）$的拓扑表示的张量类别，以便$ v $，其双重表示和伴随表示$ gl（v）$是此类别的对象。这使其成为了有限维级的有限维模块类别的类似物。我们的主要结果是，该类别是抗征品单类类别的抗征性类别，类别是张量代数的张量表示。
The Lie algebra $gl(V)$ is the Lie algebra of all endomorphisms of a countable-dimensional complex vector space $V$. We define a tensor category of topological representations of the Lie algebra $gl(V)$, so that $V$, its dual and the adjoint representation $gl(V)$ are objects of this category. This makes it an analogue of the category of finite-dimensional modules over the finite-dimensional Lie algebra $gl(n)$. Our main result is that this category is antiequivalent as a symmetric monoidal category to the category of tensor representations of the Lie algebra of finitary infinite matrices.
