论文标题
Quantum Euclidean组的Heisenberg及其表示形式
The Heisenberg double of the quantum Euclidean group and its representations
论文作者
论文摘要
量子Euclidean组的Heisenberg双$ D_Q（E_2）$ $ \ MATHCAL {O} _Q（E_2）$是$ \ Mathcal {O} _Q（E_2）$的Smash产品，其Hopf Dual $ u_q（\ Mathfrak）$对于代数$ d_q（e_2）$，可获得其素数，原始和最大光谱的明确描述。 $ D_Q（E_2）$的所有主要因素均以广义Weyl代数呈现。结果，我们获得了代数$ d_q（e_2）$没有有限维表示，并且$ d_q（e_2）$不能具有HOPF代数结构。确定了欧几里得组及其海森伯格双重的量子群体的自动形态群体。通过发电机和定义关系明确描述了一些中心化。这使我们能够对简单的权重模块进行分类，并在代数$ d_q（e_2）$上对所谓的$ a $加权模块进行分类。
The Heisenberg double $D_q(E_2)$ of the quantum Euclidean group $\mathcal{O}_q(E_2)$ is the smash product of $\mathcal{O}_q(E_2)$ with its Hopf dual $U_q(\mathfrak{e}_2)$. For the algebra $D_q(E_2)$, explicit descriptions of its prime, primitive, and maximal spectra are obtained. All prime factors of $D_q(E_2)$ are presented as generalized Weyl algebras. As a result, we obtain that the algebra $D_q(E_2)$ has no finite-dimensional representations, and that $D_q(E_2)$ cannot have a Hopf algebra structure. The automorphism groups of the quantum Euclidean group and its Heisenberg double are determined. Some centralizers are explicitly described via generators and defining relations. This enables us to give a classification of simple weight modules, and the so-called $a$-weight modules, over the algebra $D_q(E_2)$.
