Ambidextrous objects and trace functions for nonsemisimple categories

By Nathan Geer, Jonathan R. Kujawa, Bertrand Patureau-Mirand. 2011

62 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/49ab7ff1325af7ffe52487b259ad4bdcb3bf5223

How researchers see this paper

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In Geometry and Topology

1. Nathan Geer
2. Bertrand Patureau-Mirand
3. Alexis Virelizier
4. Jonathan R. Kujawa
5. G. Bòhm
6. Kenichi Shimizu

In Mathematical Physics

1. Nathan Geer
2. Bertrand Patureau-Mirand
3. Alexis Virelizier
4. G. Bòhm
5. Kenichi Shimizu

Citations in the corpus

• Traces on ideals in pivotal categories (2011, methodology): “In [4] the results of this paper are used to prove that traces on the ideal of projective modules exist for factorizable ribbon Hopf algebras, modular representations of finite groups and their quantum doubles, complex and modular Lie (super)algebras, the .”