标题： 向后映射与相关非交换向量丛的非平凡性 显示英文标题

标题： Pullbacks and nontriviality of associated noncommutative vector bundles

摘要： 我们的主要定理是：由量子主丛的等变映射诱导的相伴非交换向量丛的拉回是一个由结构性量子群的相同有限维表示所关联的非交换向量丛。 在$K_{0}$-群的层面上，我们通过显式矩阵幂等元的拉回实现诱导映射。 我们还展示了如何将我们的结果推广到量子群表示是无限维的情形，并将其应用于Ehresmann-Schauenburg量子群oid。 最后，利用非交换Milnor的联结构造，我们定义了量子四元数射影空间以及相伴的非交换切比雪夫线丛及其对偶。 作为主要定理的一个关键应用，我们证明了这些丛作为非交换复向量丛是稳定不可约的。 显示英文摘要

摘要： Our main theorem is that the pullback of an associated noncommutative vector bundle induced by an equivariant map of quantum principal bundles is a noncommutative vector bundle associated via the same finite-dimensional representation of the structural quantum group. On the level of $K_{0}$-groups, we realize the induced map by the pullback of explicit matrix idempotents. We also show how to extend our result to the case when the quantum-group representation is infinite dimensional, and then apply it to the Ehresmann-Schauenburg quantum groupoid. Finally, using noncommutative Milnor's join construction, we define quantum quaternionic projective spaces together with noncommutative tautological quaternionic line bundles and their duals. As a key application of the main theorem, we show that these bundles are stably non-trivial as noncommutative complex vector bundles.