量子超对称对与经由$\mathrm i$Hopf代数的Serre关系
Quantum supersymmetric pairs and the Serre relations via $\mathrm i$Hopf algebras
- Shantou University（汕头大学）
- Xiamen University（厦门大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文研究基本型量子超群的iHopf代数，通过Borel量子群实现量子超对称对，推导iHopf乘法与原始乘法的转换公式，并刻画拟分裂iquantum超群中的全部Serre关系。
AI中文摘要：
我们研究基本型量子超群相关的iHopf代数。对于量子超对称对$(\mathbf{U}, \mathbf{U}^\imath)$，我们将$\mathbf{U}^\imath$和$\mathbf{U}$分别实现为Borel量子群${\hat{\mathbf{U}}}_q^{\geq0}$与张量积代数${\hat{\mathbf{U}}}_q^{\geq0}\otimes {\hat{\mathbf{U}}}_q^{\geq0}$的iHopf代数，而余理想子代数结构由iHopf代数之间的嵌入编码。此外，我们推导出iHopf乘法与原始乘法之间的显式转换公式，该公式提供了一种将量子（超）群的定义关系转化为iquantum（超）群关系的一般机制。特别地，基本型拟分裂iquantum超群中出现的所有Serre关系均被刻画。
英文摘要：
We study iHopf algebras associated with quantum supergroups of basic type. For a quantum supersymmetric pair $(\mathbf{U}, \mathbf{U}^\imath)$, we realize $\mathbf{U}^\imath$ and $\mathbf{U}$ as the iHopf algebras of the Borel quantum group ${\hat{\mathbf{U}}}_q^{\geq0}$ and the tensor product algebra ${\hat{\mathbf{U}}}_q^{\geq0}\otimes {\hat{\mathbf{U}}}_q^{\geq0}$, respectively, while the coideal subalgebra structure is encoded by an embedding between the iHopf algebras. Moreover, we derive an explicit conversion formula between the iHopf multiplication and the original multiplication, which provides a general mechanism transforming the defining relations of quantum (super)groups into relations of iquantum (super)groups. In particular, all the Serre relations that occur in quasi-split iquantum supergroups of basic type are characterized.
