论文标题
在约旦飞机双重的有限维度上
On the finite-dimensional representations of the double of the Jordan plane
论文作者
论文摘要
我们继续研究约旦飞机的德林菲尔德双重，并用$ \ Mathcal d $表示，并在Arxiv：2002.02514中引入。 简单的有限维模块是在Arxiv中计算的：2108.13849；事实证明，它们通过$ u（\ spl_2（\ bbbk））$分解。在这里，我们介绍了Verma模块和类别$ \ Mathfrak o $，用于$ \ Mathcal D $，它们与谎言理论中的类似模块相似，但是由三角分解的0部分的不可兼容的模块引起的。因此，有最高权重等级（HW-RK）的概念。 我们对HW-RK一个不可分解的模块进行了分类，并找到了HW-RK两个的家族。 $ \ Mathcal D $的Gabriel颤抖是计算出来的，这意味着它具有野生表示类型。
We continue the study of the Drinfeld double of the Jordan plane, denoted by $\mathcal D$ and introduced in arXiv:2002.02514. The simple finite-dimensional modules were computed in arXiv:2108.13849; it turns out that they factorize through $U(\spl_2(\Bbbk))$. Here we introduce the Verma modules and the category $\mathfrak O$ for $\mathcal D$, which have a resemblance to the similar ones in Lie theory but induced from indecomposable modules of the 0-part of the triangular decomposition. Accordingly, there is the notion of highest weight rank (hw-rk). We classify the indecomposable modules of hw-rk one and find families of hw-rk two. The Gabriel quiver of $\mathcal D$ is computed implying that it has a wild representation type.
