标题： 拉回非交换相关向量丛 显示英文标题

标题： Pulling back noncommutative associated vector bundles

摘要： 对于余代数$\mathcal{C}$的任何有限维核心表示$V$，该核心表示在代数$\mathcal{A}$上主要作用，我们可以构造一个与之相关的在共作用不变子代数$\mathcal{B}$上的有限生成投射模$\mathcal{A}\Box^\mathcal{C} V$。 该模$\mathcal{A}\Box^\mathcal{C} V$是相关非交换向量丛的截面模。 如果 $\mathcal{A}'$ 是一个具有 $\mathcal{C}$ 主余作用的代数，且 $\mathcal{B'}$ 是其余作用不变子代数，那么任何等变（共线）代数同态 $\mathcal{A}\to\mathcal{A}'$ 都会限制并核心限制为一个代数同态 $\mathcal{B}\to\mathcal{B}'$，使得 $\mathcal{B}'$ 成为一个 $(\mathcal{B}'-\mathcal{B})$-双模。 我们的主要结果是有限生成的左$\mathcal{B}'$-模$\mathcal{B}'\otimes_\mathcal{B}(\mathcal{A}\Box^\mathcal{C} V)$和$\mathcal{A}'\Box^\mathcal{C} V$是同构的。 作为推论，我们得出结论，对于任何在赋予紧致量子群自由作用的单位C*-代数之间的等变*-同态$f:A\to A'$，假设在$A$上的作用是自由的，所诱导的K理论映射$f_*\colon K_0(B)\to K_0(B')$，其中$B$和$B'$是相应的固定点子代数，满足$f_*([A\Box^\mathcal{C} V])=[A'\Box^\mathcal{C} V]$。 作为一项关键应用，我们证明了任何有限次迭代的等变非交换连接的$SU_q(2)$与自身的连接作为$SU_q(2)$-紧量子主丛不是可平凡化的。 我们还展示了如何将我们的结果扩展到$V$是无限维的情况，然后将其应用于 Ehresmann-Schauenburg 量子群胚。 显示英文摘要

摘要： For any finite-dimensional corepresentation $V$ of a coalgebra $\mathcal{C}$ coacting principally on an algebra $\mathcal{A}$, we can form an associated finitely generated projective module $\mathcal{A}\Box^\mathcal{C} V$ over the coaction-invariant subalgebra $\mathcal{B}$. The module $\mathcal{A}\Box^\mathcal{C} V$ is the section module of the associated noncommutative vector bundle. If $\mathcal{A}'$ is an algebra with a principal coaction of $\mathcal{C}$ and $\mathcal{B'}$ is its coaction-invariant subalgebra, then any equivariant (colinear) algebra homomorphism $\mathcal{A}\to\mathcal{A}'$ restricts and corestricts to an algebra homomorphism $\mathcal{B}\to\mathcal{B}'$ making $\mathcal{B}'$ a $(\mathcal{B}'-\mathcal{B})$-bimodule. Our main result is that the finitely generated left $\mathcal{B}'$-modules $\mathcal{B}'\otimes_\mathcal{B}(\mathcal{A}\Box^\mathcal{C} V)$ and $\mathcal{A}'\Box^\mathcal{C} V$ are isomorphic. As a corollary, we conclude that, for any equivariant *-homomorphism $f:A\to A'$ between unital C*-algebras equipped with a free action of a compact quantum group, assuming freeness of the action on $A$, the induced K-theory map $f_*\colon K_0(B)\to K_0(B')$, where $B$ and $B'$ are the respective fixed-point subalgebras, satisfies $f_*([A\Box^\mathcal{C} V])=[A'\Box^\mathcal{C} V]$. As a key application, we show that any finitely-iterated equivariant noncommutative join of $SU_q(2)$ with itself is not trivializable as an $SU_q(2)$-compact quantum principal bundle. We also show how to extend our result to the case when $V$ is infinitely dimensional, and then apply it to the Ehresmann-Schauenburg quantum groupoid.