Aligned CP-Semigroups

Christopher Jankowski; Daniel Markiewicz; Robert T. Powers

doi:10.1093/imrn/rnu138

Aligned CP-Semigroups

Christopher Jankowski
, Daniel Markiewicz
, Robert T. Powers

Department of Mathematics

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

2 Scopus citations

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	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

ASJC Scopus subject areas

General Mathematics

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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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AU - Jankowski, Christopher

AU - Markiewicz, Daniel

AU - Powers, Robert T.

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N2 - 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.

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.

UR - https://www.scopus.com/pages/publications/84939605004

U2 - 10.1093/imrn/rnu138

DO - 10.1093/imrn/rnu138

M3 - Article

AN - SCOPUS:84939605004

SN - 1073-7928

VL - 2015

SP - 6639

EP - 6647

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

IS - 15

ER -

Aligned CP-Semigroups

Abstract

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