乘法Gerbe上的Pontrjagin对偶
Pontrjagin duality on multiplicative Gerbes
AI总结：
该研究基于拓扑群的Segal-Mitchison上同调构建拓扑gerbe模型，引入乘法gerbe及其表示，证明Pontrjagin对偶乘法gerbe的表示范畴与幺半中心均等价，并给出多类群上的实例。
摘要：
我们利用拓扑群的Segal-Mitchison上同调，为拓扑gerbe定义了一个便于使用的模型。在此框架下，我们引入了拓扑群上的乘法gerbe，并定义了其表示。针对一类特定的表示，我们构造了它的自同态范畴，并证明该范畴会在另一个拓扑群上诱导出一个新的乘法gerbe。这个新诱导出的群在纤维层面是原群的Pontrjagin对偶，因此我们将这对乘法gerbe称为“Pontrjagin对偶”。我们证明Pontrjagin对偶乘法gerbe具有等价的表示范畴，此外还证明它们的幺半中心也是等价的。文中还给出了有限群、离散群，以及紧与非紧李群上的Pontrjagin对偶乘法gerbe的例子。
英文摘要：
We use Segal-Mitchison's cohomology of topological groups to define a convenient model for topological gerbes. We introduce multiplicative gerbes over topological groups in this setup and we define its representations. For a specific choice of representation, we construct its category of endomorphisms and we show that it induces a new multiplicative gerbe over another topological group. This new induced group is fibrewise Pontrjagin dual to the original one and therefore we called the pair of multiplicative gerbes `Pontrjagin dual'. We show that Pontrjagin dual multipliciative gerbes have equivalent categories of representations and moreover, we show that their monoidal centers are equivalent. Examples of Pontrjagin dual multiplicative gerbes over finite and discrete, as well as compact and non-compact Lie groups are provided.
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。
