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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Probabilistically nilpotent Hopf algebras
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by Miriam Cohen and Sara Westreich PDF
Trans. Amer. Math. Soc. 368 (2016), 4295-4314 Request permission


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:
  • Sara Westreich
  • Affiliation: Department of Management, Bar-Ilan University, Ramat-Gan, Israel
  • Email:
  • 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:
  • MathSciNet review: 3453372