Product systems over Ore monoids

Albandik, Suliman; Meyer, Ralf

doi:10.48550/arxiv.1502.07768

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Ore Monoids1

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2022

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“…Product systems of C*-correspondences (Hilbert bimodules) over Ore monoids have been studied independently by Albandik and Meyer [3] and Kwaśniewski and Szymański [27]. Albandik and Meyer's definitions are slightly more general, because they allow also noncancellative monoids.…”

Section: Ore Monoidsmentioning

confidence: 99%

Categorial Independence and Lévy Processes

Gerhold¹,

Lachs²,

Schürmann³

2022

SIGMA

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We generalize Franz' independence in tensor categories with inclusions from two morphisms (which represent generalized random variables) to arbitrary ordered families of morphisms. We will see that this only works consistently if the unit object is an initial object, in which case the inclusions can be defined starting from the tensor category alone. The obtained independence for morphisms is called categorial independence. We define categorial Lévy processes on every tensor category with initial unit object and present a construction generalizing the reconstruction of a Lévy process from its convolution semigroup via the Daniell-Kolmogorov theorem. Finally, we discuss examples showing that many known independences from algebra as well as from (noncommutative) probability are special cases of categorial independence.

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Section: Ore Monoidsmentioning

confidence: 99%