标题： 非交换T对偶性的群论方法 显示英文标题

标题： A groupoid approach to noncommutative T-duality

摘要： 拓扑T对偶性是一种将主环面丛上的gerbe转换为主对偶环面丛上的gerbe的变换。 我们提供了一种新的T对偶化几何构造，这使得对偶性可以扩展到以下两个方向。 首先，除了环面之外的群的丛，甚至某些非阿贝尔群的丛也可以进行对偶。 其次，其对偶为非交换群族（在非交换几何的意义上）的丛可以被处理，尽管在这种情况下，丛的基空间最好被视为一个拓扑堆栈。 用于构造的一些方法可能具有独立的兴趣。 这些包括一种交换阿贝尔主丛与gerbe的庞特里亚金型对偶，一种用于范畴的非阿贝尔塔基类型对偶，以及某些等变布劳尔群的计算。 显示英文摘要

摘要： Topological T-duality is a transformation taking a gerbe on a principal torus bundle to a gerbe on a principal dual-torus bundle. We give a new geometric construction of T-dualization, which allows the duality to be extended in following two directions. First, bundles of groups other than tori, even bundles of some nonabelian groups, can be dualized. Second, bundles whose duals are families of noncommutative groups (in the sense of noncommutative geometry) can be treated, though in this case the base space of the bundles is best viewed as a topological stack. Some methods developed for the construction may be of independent interest. These are a Pontryagin type duality that interchanges commutative principal bundles with gerbes, a nonabelian Takai type duality for groupoids, and the computation of certain equivariant Brauer groups.