Probabilistically nilpotent Hopf algebras

Cohen, Miriam; Westreich, Sara

doi:10.1090/tran/6462

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 which depends only on the Grothendieck ring of When 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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