Generalized trace and modified dimension functions on ribbon categories

Details Generalized trace and modified dimension functions on ribbon categories Generalized trace and modified dimension functions on ribbon categories

2010-01-06

arxiv.org/abs/1001.0985v1

Mathematics

Representation Theory

44 pages

Scientific paper

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 non-zero. 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.

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