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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Probabilistically nilpotent Hopf algebras

Authors: Miriam Cohen and Sara Westreich
Journal: Trans. Amer. Math. Soc. 368 (2016), 4295-4314
MSC (2000): Primary 16T05
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

Sara Westreich
Affiliation: Department of Management, Bar-Ilan University, Ramat-Gan, Israel

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