论文标题
Pontrjagin二元性在乘法Gerbes上
Pontrjagin duality on multiplicative Gerbes
论文作者
论文摘要
我们使用Segal-Mitchison的拓扑组共同体来定义拓扑ger的方便模型。我们在此设置中介绍了倍增组的乘法gerbes，并定义了其表示形式。对于特定的表示形式选择，我们构建了其内态性类别，并表明它诱导了一个新的乘法gerbe，而不是另一个拓扑组。这个新的诱导组是纤维中的pontrjagin dual dual to原始组，因此我们称这对乘法gerbes`pontrjagin dual dual''。我们表明，pontrjagin双重多重gerbes具有等效的表示类别，而且我们表明它们的单体中心是等效的。提供了Pontrjagin双重乘法Gerbes在有限和离散以及紧凑型和非压缩谎言组上的示例。
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.
