量子实射影空间上的量子主丛
Quantum principal bundles over quantum real projective spaces
摘要：
构造了量子实射影空间上的两类量子主丛。一个层次包含以U（1）为结构群的丛，另一个层次以量子群$SU_q(2)$为纤维。这两个层次得到的过程中延长从丛的循环群的阶2作为纤维。这些丛的平凡性或其他方面是通过使用一个一般的标准确定的一个扩张的余模代数是一个分裂的霍普夫-伽罗瓦扩张。
英文摘要：
Two hierarchies of quantum principal bundles over quantum real projective spaces are constructed. One hierarchy contains bundles with U(1) as a structure group, the other has the quantum group $SU_q(2)$ as a fibre. Both hierarchies are obtained by the process of prolongation from bundles with the cyclic group of order 2 as a fibre. The triviality or otherwise of these bundles is determined by using a general criterion for a prolongation of a comodule algebra to be a cleft Hopf-Galois extension.
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。
