Free-free-Boolean independence for triples of algebras

In this paper, we introduce the notion of free-free-Boolean independence relation for triples of algebras. We define free-free-Boolean cumulants ans show that the vanishing of mixed cumulants is equivalent to free-free-Boolean independence. A free-free -Boolean central limit law is studied.
Comment: 21 pages+ reference. Comments are welcome. arXiv admin note: text overlap with arXiv:1710.01374