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 | References | Similar Articles | Additional Information
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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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