2002/06/27 by Frederick M. Goodman, Goodman, Frederick M.
Computer Science · Mathematics · #46L53 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #Polynomial and algebraic computation #Probability (math.PR) #math.OA #math.PR #msc:46L53
paper · pdf · doi:10.48550/arxiv.math/0206296
16 pages, Latex. Minor revision
openalex publication_date 2002/06/27 · arxiv created 2002/07/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We generalize results of Mingo and Nica on graded independence from the context of \mathbb Z2--graded (Fermionic) noncommutative probability spaces to that of \mathbb Zn--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 Zn--graded independent random variables.