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arXiv · 1912.07831

The applications of probability groups on Hopf algebras

Jingheng Zhou·Shenglin Zhu
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Abstract

In this work, we use probability groups, introduced by Harrison in 1979, as a tool to study a semisimple Hopf algebra $H$ with a commutative character ring and prove that the algebra generalized by the dual probability group is the center $Z(H)$ of $H$ and the product of two class sums is an integral combination up to a factor of $\dim (H)^{-1}$ of the class sums of $H$. We classify all the 2-integral probability groups with 2 or 3 elements.

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Jingheng Zhou, Shenglin Zhu. 2020-08-04. The applications of probability groups on Hopf algebras. https://doi.org/10.1080/00927872.2020.1791897

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