Aligned CP-Semigroups

Christopher Jankowski; Daniel Markiewicz; Robert T. Powers

doi:https://doi.org/10.1093/imrn/rnu138

Aligned CP-Semigroups

Christopher Jankowski, Daniel Markiewicz, Robert T. Powers

Department of Mathematics

Ben-Gurion University of the Negev

Research output: Contribution to journal › Article › peer-review

Abstract

A CP-semigroup is aligned if its set of trivially maximal subordinates is totally ordered by subordination. We prove that aligned spatial E₀-semigroups are prime: they have no nontrivial tensor product decompositions up to cocycle conjugacy. As a consequence, we establish the existence of uncountably many noncocycle conjugate E₀-semigroups of type II₀ which are prime.

Original language	American English
Pages (from-to)	6639-6647
Number of pages	9
Journal	International Mathematics Research Notices
Volume	2015
Issue number	15
DOIs	https://doi.org/10.1093/imrn/rnu138
State	Published - 1 Jan 2015

All Science Journal Classification (ASJC) codes

General Mathematics

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https://doi.org/10.1093/imrn/rnu138

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title = "Aligned CP-Semigroups",

abstract = "A CP-semigroup is aligned if its set of trivially maximal subordinates is totally ordered by subordination. We prove that aligned spatial E0-semigroups are prime: they have no nontrivial tensor product decompositions up to cocycle conjugacy. As a consequence, we establish the existence of uncountably many noncocycle conjugate E0-semigroups of type II0 which are prime.",

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AB - A CP-semigroup is aligned if its set of trivially maximal subordinates is totally ordered by subordination. We prove that aligned spatial E0-semigroups are prime: they have no nontrivial tensor product decompositions up to cocycle conjugacy. As a consequence, we establish the existence of uncountably many noncocycle conjugate E0-semigroups of type II0 which are prime.

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Aligned CP-Semigroups

Abstract

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