Probabilistically nilpotent Hopf algebras
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- by Miriam Cohen and Sara Westreich PDF
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Abstract:
In this paper we investigate nilpotenct and probabilistically nilpotent Hopf algebras. We define nilpotency via a descending chain of commutators and give a criterion for nilpotency via a family of central invertible elements. These elements can be obtained from a commutator matrix $A$ which depends only on the Grothendieck ring of $H.$ When $H$ is almost cocommutative we introduce a probabilistic method. We prove that every semisimple quasitriangular Hopf algebra is probabilistically nilpotent. In a sense we thereby answer the title of our paper Are we counting or measuring anything? by Yes, we are.References
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Additional Information
- Miriam Cohen
- Affiliation: Department of Mathematics, Ben Gurion University of the Negev, Beer Sheva, Israel
- Email: mia@math.bgu.ac.il
- Sara Westreich
- Affiliation: Department of Management, Bar-Ilan University, Ramat-Gan, Israel
- Email: swestric@biu.ac.il
- Received by editor(s): September 25, 2013
- Received by editor(s) in revised form: April 24, 2014
- Published electronically: September 15, 2015
- Additional Notes: This research was supported by the Israel Science Foundation, 170-12.
- © Copyright 2015 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 368 (2016), 4295-4314
- MSC (2000): Primary 16T05
- DOI: https://doi.org/10.1090/tran/6462
- MathSciNet review: 3453372