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arXiv 0908.1563math.QAmath.RT
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上循环扭下的Yetter-Drinfeld模

Yetter-Drinfeld modules under cocycle twists

Georgia Benkart, Mariana Pereira, Sarah Witherspoon

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19 pages, minor revisions, to appear in Journal of Algebra
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摘要：

给出了有限维点霍普夫代数$H$的单Yetter-Drinfeld模与$H$的上圈扭$H^σ$的单Yetter-Drinfeld模之间的对应关系的一个显式.这意味着它们的德林费尔德双精度模之间是等价的。为了说明我们的结果，我们考虑限制的双参数量子群${\mathfrak{u}}_{r,s}({\mathfrak{sl}}_n)$的条件下的参数保证${\mathfrak{u}}_{r,s}({\mathfrak{sl}}_n)$是一个Drinfeld双的Borel子代数。我们确定明确的对应关系之间的${\mathfrak{u}}_{r,s}({\mathfrak{sl}}_n)$ -模块为不同的值的$r$和$s$，并提供例子，没有这样的对应关系可以存在。我们的例子是通过计算机代数系统{ \sc Singular：：Plural}获得的。

英文摘要：

We give an explicit formula for the correspondence between simple Yetter-Drinfeld modules for certain finite-dimensional pointed Hopf algebras $H$ and those for cocycle twists $H^σ$ of $H$. This implies an equivalence between modules for their Drinfeld doubles. To illustrate our results, we consider the restricted two-parameter quantum groups ${\mathfrak{u}}_{r,s}({\mathfrak{sl}}_n)$ under conditions on the parameters guaranteeing that ${\mathfrak{u}}_{r,s}({\mathfrak{sl}}_n)$ is a Drinfeld double of its Borel subalgebra. We determine explicit correspondences between ${\mathfrak{u}}_{r,s}({\mathfrak{sl}}_n)$-modules for different values of $r$ and $s$ and provide examples where no such correspondence can exist. Our examples were obtained via the computer algebra system {\sc Singular::Plural}.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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