关于酉Jordan双模的Tits-Kantor-Koecher构造
On the Tits-Kantor-Koecher construction of unital Jordan bimodules
摘要：
本文研究了Jordan代数$\J$的表示与由$\J$通过Tits-Kantor-Koecher构造得到的李代数$\g$之间的关系.更准确地说，我们构造了两个伴随函子$Lie :\JJ\to \ggm$和$Jor:\ggm\to\JJ$，其中$\JJ$是单位$\J$ -双模的范畴，$\ggm$是允许短分次的$\g$ -模的范畴.利用这些函子，我们对$\J$进行了分类，使得它的半单部分是Clifford型的，并且范畴$\JJ$是驯服的.
英文摘要：
In this paper we explore relationship between representations of a Jordan algebra $\J$ and the Lie algebra $\g$ obtained from $\J$ by the Tits-Kantor-Koecher construction. More precisely, we construct two adjoint functors $Lie :\JJ\to \ggm$ and $Jor:\ggm\to\JJ$, where $\JJ$ is the category of unital $\J$-bimodules and $\ggm$ is the category of $\g$-modules admitting a short grading. Using these functors we classify $\J$ such that its semisimple part is of Clifford type and the category $\JJ$ is tame.
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