Ambidextrous objects and trace functions for nonsemisimple categories

Details Ambidextrous objects and trace functions for nonsemisimple categories Ambidextrous objects and trace functions for nonsemisimple categories

2011-06-22

arxiv.org/abs/1106.4477v3

Mathematics

Representation Theory

15 pages, title changed, other minor changes, to appear in the Proceedings of the American Mathematical Society

Scientific paper

We provide a necessary and sufficient condition for a simple object in a pivotal k-category to be ambidextrous. In turn, these objects imply the existence of nontrivial trace functions in the category. These functions play an important role in low-dimensional topology as well as in studying the category itself. In particular, we prove they exist for factorizable ribbon Hopf algebras, modular representations of finite groups and their quantum doubles, complex and modular Lie (super)algebras, the $(1,p)$ minimal model in conformal field theory, and quantum groups at a root of unity.

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