使用$\scr O_0$中的infinite-dimensional模块进行张紧
Tensoring with infinite-dimensional modules in $\scr O_0$
摘要：
证明了半单李代数$\germ g$的BGG范畴$\scr O$的主块$\scr O_0$通过保持倾斜模的正合内函子、保持投射模的右正合内函子和保持内射模的左正合内函子忠实地作用于自身.所有这些函子的起源是张量与范畴$\scr O$中的任意（不一定是有限维）模。我们研究这样的函子，描述他们的伴随，并表明，他们给$\scr O_0$上产生一个自然的（co）单子结构。此外，所有这一切推广到抛物线子范畴的$\scr O_0$。作为一个例子，我们给出了代数$\germ{sl}_3$的一些显式计算。
英文摘要：
We show that the principal block $\scr O_0$ of the BGG category $\scr O$ for a semisimple Lie algebra $\germ g$ acts faithfully on itself via exact endofunctors which preserve tilting modules, via right exact endofunctors which preserve projective modules and via left exact endofunctors which preserve injective modules. The origin of all these functors is tensoring with arbitrary (not necessarily finite-dimensional) modules in the category $\scr O$. We study such functors, describe their adjoints and show that they give rise to a natural (co)monad structure on $\scr O_0$. Furthermore, all this generalises to parabolic subcategories of $\scr O_0$. As an example, we present some explicit computations for the algebra $\germ{sl}_3$.
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