Probabilistically nilpotent Hopf algebras
Quantum Algebra
2013-09-30 v1
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 {\it 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 {\it Are we counting or measuring anything?} by {\it Yes we are}.
Cite
@article{arxiv.1309.7115,
title = {Probabilistically nilpotent Hopf algebras},
author = {M. Cohen and S. Westreich},
journal= {arXiv preprint arXiv:1309.7115},
year = {2013}
}