论文标题
部分可观测时空混沌系统的无模型预测
The Green ring of a family of copointed Hopf algebras
论文作者
论文摘要
Fomin-Kirillov代数$ \ MATHCAL {FK} _3 $在对称组$ \ MATHBB {S} _3 $上的代数上的共同提升是由Andruskiewitsch和作者分类的。我们在这里证明，与通用参数相关的那些相当于众所周知的Hopf代数的非简单块：Taft代数的Drinfeld双打和小量子组$ u_ {q}（Q}（\ Mathfrak {slfrak {sl}} _2）_2）$。这些模块上的不可分解的模块由Chen，Chari--premet和Suter独立地分类。因此，我们在$ \ Mathcal {fk} _3 $的通用升降机上获得了insocompososable模块。我们将它们之间的张量产品分解为不可分解的模块的直接总和。然后，我们推断出发电机的演讲和绿环的关系。
The copointed liftings of the Fomin-Kirillov algebra $\mathcal{FK}_3$ over the algebra of functions on the symmetric group $\mathbb{S}_3$ were classified by Andruskiewitsch and the author. We demonstrate here that those associated to a generic parameter are Morita equivalent to the non-simple blocks of well-known Hopf algebras: the Drinfeld doubles of the Taft algebras and the small quantum groups $u_{q}(\mathfrak{sl}_2)$. The indecomposable modules over these were classified independently by Chen, Chari--Premet and Suter. Consequently, we obtain the indocomposable modules over the generic liftings of $\mathcal{FK}_3$. We decompose the tensor products between them into the direct sum of indecomposable modules. We then deduce a presentation by generators and relations of the Green ring.
