论文标题
类别$ \ MATHCAL {O} $用于root-reductive Lie代数：II。翻译函子和倾斜模块
Categories $\mathcal{O}$ for Root-Reductive Lie Algebras: II. Translation Functors and Tilting Modules
论文作者
论文摘要
这是针对类别的版本$ \ mathcal {o} $的第二篇论文的第二篇论文，用于root-reductive lie代数。令$ \ mathfrak {g} $成为一个词根谎言代数，在代数封闭的字段$ \ mathbb {k} $中，具有特征性$ 0 $的$ 0 $，带有分裂的borel subalgebra $ \ mathfrak {b} $，其中包含最大的Maximal toral subalgebra $ \ mathfrak $ \} $}。对于一些块，$ \ overline {\ Mathcal {o}} [λ] $和$ \ overline {\ Mathcal {o}} [μ] $，其对象具有有限长度的子类别是通过函数通过型的指挥限制来获得的函数的等价。倾斜对象也可以在$ \ overline {\ mathcal {o}} $中定义。也有与有限维情况并行的通用倾斜对象$ d（λ）$。
This is the second paper of a series of papers on a version of categories $\mathcal{O}$ for root-reductive Lie algebras. Let $\mathfrak{g}$ be a root-reductive Lie algebra over an algebraically closed field $\mathbb{K}$ of characteristic $0$ with a splitting Borel subalgebra $\mathfrak{b}$ containing a splitting maximal toral subalgebra $\mathfrak{h}$. For some pairs of blocks $\overline{\mathcal{O}}[λ]$ and $\overline{\mathcal{O}}[μ]$, the subcategories whose objects have finite length are equivalence via functors obtained by the direct limits of translation functors. Tilting objects can also be defined in $\overline{\mathcal{O}}$. There are also universal tilting objects $D(λ)$ in parallel to the finite-dimensional cases.
