论文标题
双线性配对在二维同居和脱口机类别的概括性上
Bilinear pairings on two-dimensional cobordisms and generalizations of the Deligne category
论文作者
论文摘要
对称组的deligne类别是分区类别的添加剂karoubi关闭。对于参数t的通用值，它是半体间的，而当t是一个非负整数时，当通过可忽略不计的形态的理想中，产生对称组的表示类别。可以通过特定的二维恢复类别的线性化来解释分区类别。 Deligne类别及其半圣经的商也接受了类似的解释。这种观点与二维拓扑理论的通用结构相结合，导致该分区和deligne类别的多参数单体概括，一个在一个变量中用于每个理性函数。
The Deligne category of symmetric groups is the additive Karoubi closure of the partition category. It is semisimple for generic values of the parameter t while producing categories of representations of the symmetric group when modded out by the ideal of negligible morphisms when t is a non-negative integer. The partition category may be interpreted, following Comes, via a particular linearization of the category of two-dimensional oriented cobordisms. The Deligne category and its semisimple quotients admit similar interpretations. This viewpoint coupled to the universal construction of two-dimensional topological theories leads to multi-parameter monoidal generalizations of the partition and the Deligne categories, one for each rational function in one variable.
