Abstract
In this paper we study the states of Poisson type and infinitely divisible states on compact quantum groups. Each state of Poisson type is infinitely divisible, i.e., it admits n-th root for all nge 1. The main result is that on finite quantum groups infinitely divisible states must be of Poisson type. This generalizes Böge’s theorem concerning infinitely divisible measures (commutative case) and Parthasarathy’s result on infinitely divisible positive definite functions (cocommutative case). Two proofs are given.
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