Free-Boolean independence for pairs of algebras

2017/10/03 by Weihua Liu, Liu, Weihua · 1 citation
Computer Science · Mathematics · #Advanced Algebra and Logic #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.1710.01374

openalex publication_date 2017/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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