Free-Boolean independence for pairs of algebras
arXiv:1710.01374
Abstract
We construct pairs of algebras with mixed independence relations by using truncations of reduced free products of algebras. For example, we construct free-Boolean pairs of algebras and free-monotone pairs of algebras. We also introduce free-Boolean cumulants and show that free-Boolean independence is equivalent to the vanishing of mixed cumulants.
Moments-condition for free-Boolean independence is added to Section 4. Title is changed. All comments are welcome