Generalized trace and modified dimension functions on ribbon categories
Generalized trace and modified dimension functions on ribbon categories
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功能区类别上的广义追踪和修改尺寸函数
DOI：
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发表时间：
2010
期刊：
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通讯作者：
Bertrand Patureau
中科院分区：
文献类型：
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作者：
Nathan Geer;J. Kujawa;Bertrand Patureau
本文利用拓扑技巧构造了某些带范畴理想上的广义迹和修正维数函数。这样的带状范畴的例子自然出现在表示论中，其中通常的迹和维数函数为零，但这些广义的迹和修正的维数函数是非零的。这样的例子包括某些李代数和有限群在正特征域上的有限维模的范畴和复数上的基本李超代数的有限维模的范畴。这些修正的维度可以被分类地解释，并且与表征理论的一些基本概念密切相关。
In this paper, we use topological techniques to construct generalized trace and modified dimension functions on ideals in certain ribbon categories. Examples of such ribbon categories naturally arise in representation theory where the usual trace and dimension functions are zero, but these generalized trace and modified dimension functions are nonzero. Such examples include categories of finite dimensional modules of certain Lie algebras and finite groups over a field of positive characteristic and categories of finite dimensional modules of basic Lie superalgebras over the complex numbers. These modified dimensions can be interpreted categorically and are closely related to some basic notions from representation theory.