$\mathbb Z_n$--graded Independence

Details $\mathbb Z_n$--graded Independence $\mathbb Z_n$--graded Independence

2002-06-27

arxiv.org/abs/math/0206296v2

Mathematics

Operator Algebras

16 pages, Latex. Minor revision

Scientific paper

We generalize results of Mingo and Nica on graded independence from the context of $\mathbb Z_2$--graded (Fermionic) noncommutative probability spaces to that of $\mathbb Z_n$--graded noncommutative probability spaces. We show that for $q$ a primitive $n$-th root of unity, the $q$-cumulants defined by Nica linearize the addition of homogeneous $\mathbb Z_n$--graded independent random variables.

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