Free-Boolean independence with amalgamation
Weihua Liu, Ping Zhong
TL;DR
This paper introduces free-Boolean independence with amalgamation, develops associated cumulants, and characterizes independence through mixed moments, extending the theory within operator algebras.
Contribution
It defines free-Boolean independence with amalgamation, constructs cumulants, and characterizes independence via mixed moments in a $C^*$-algebra setting.
Findings
Vanishing mixed free-Boolean cumulants characterize independence.
Free-Boolean cumulants are constructed and analyzed.
Positivity property established over $C^*$-algebras.
Abstract
In this paper, we develop the notion of free-Boolean independence in an amalgamation setting. We construct free-Boolean cumulants and show that the vanishing of mixed free-Boolean cumulants is equivalent to our free-Boolean independence with amalgamation. We also provide a characterization of free-Boolean independence by conditions in terms of mixed moments. In addition, we study free-Boolean independence over a -algebra and prove a positivity property.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Advanced Algebra and Logic · Advanced Topics in Algebra