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This work shows how free-free-Boolean independence is connected to algebra independence and bi-free probability.
This work concerns notions of multi-algebra independence introduced by Liu and how they can be studied in the context of bi-free probability. In particular, we show how the free-free-Boolean independence for triples of algebras can be embedded intro and therefore studied from a lens of bi-free probability. It is also shown how its cumulants can be constructed from the bi-free cumulants.
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Daniel Pepper (2025) studied this question.
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