Ambidextrous objects and trace functions for nonsemisimple categories

We provide a necessary and sufficient condition for a simple object in a pivotal k-category to be ambidextrous. As a consequence we prove that 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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