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Probabilistically nilpotent Hopf algebras


Authors: Miriam Cohen and Sara Westreich
Journal: Trans. Amer. Math. Soc. 368 (2016), 4295-4314
MSC (2010): Primary 16T05
DOI: https://doi.org/10.1090/tran/6462
Published electronically: September 15, 2015
MathSciNet review: 3453372
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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.


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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

DOI: https://doi.org/10.1090/tran/6462
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.
Article copyright: © Copyright 2015 American Mathematical Society