## Abstract

This paper concerns the structure of the group of local unitary cocycles, also called the gauge group, of an E_{0}-semigroup. The gauge group of a spatial E_{0}-semigroup has a natural action on the set of units by operator multiplication. Arveson has characterized completely the gauge group of E_{0}-semigroups of type I, and as a consequence it is known that in this case the gauge group action is transitive. In fact, if the semigroup has index k, then the gauge group action is transitive on the set of (k + 1)-tuples of appropriately normalized independent units. An action of the gauge group having this property is called (k + 1)-fold transitive. We construct examples of E_{0}-semigroups of type II and index 1 which are not 2-fold transitive. These new examples also illustrate that an E_{0}-semigroup of type II_{k} need not be a tensor product of an E_{0}-semigroup of type II_{0} and another of type I_{k}.

Original language | English |
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Pages (from-to) | 1511-1543 |

Number of pages | 33 |

Journal | Journal of Functional Analysis |

Volume | 256 |

Issue number | 5 |

DOIs | |

State | Published - 1 Mar 2009 |

## Keywords

- CP-semigroup
- Cocycles
- Dilations
- E-semigroup
- Units

## ASJC Scopus subject areas

- Analysis

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