The applications of probability groups on Hopf algebras

摘要

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 two or three elements.