Ambidextrous objects and trace functions for nonsemisimple categories
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- by Nathan Geer, Jonathan Kujawa and Bertrand Patureau-Mirand PDF
- Proc. Amer. Math. Soc. 141 (2013), 2963-2978 Request permission
Abstract:
We provide a necessary and sufficient condition for a simple object in a pivotal $\Bbbk$-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.References
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Additional Information
- Nathan Geer
- Affiliation: Department of Mathematics and Statistics, Utah State University, Logan, Utah 84322
- Email: nathan.geer@usu.edu
- Jonathan Kujawa
- Affiliation: Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019
- MR Author ID: 720815
- Email: kujawa@math.ou.edu
- Bertrand Patureau-Mirand
- Affiliation: LMAM, Université de Bretagne-Sud, Université Européenne de Bretagne, BP 573, 56017 Vannes, France
- Email: bertrand.patureau@univ-ubs.fr
- Received by editor(s): June 22, 2011
- Received by editor(s) in revised form: November 15, 2011
- Published electronically: May 10, 2013
- Additional Notes: Research of the first author was partially supported by NSF grants DMS-0968279 and DMS-1007197.
Research of the second author was partially supported by NSF grant DMS-0734226 and NSA grant H98230-11-1-0127. - Communicated by: Kailash E. Misra
- © Copyright 2013 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 141 (2013), 2963-2978
- MSC (2010): Primary 18D10; Secondary 17B99, 16T05, 20C20, 57M99
- DOI: https://doi.org/10.1090/S0002-9939-2013-11563-7
- MathSciNet review: 3068949