Local unitary cocycles of Eo-semigroups

摘要

This paper concerns the structure of the group of local unitary cocycles, also called the gauge group, of an E0-semigroup. The gauge group of a spatial E0-semigroup has a natural action on the set of units by operator multiplication. Arveson has characterized completely the gauge group of E0-semigroups of type 1, 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 E0-semigroups of type 11 and index 1 which are not 2-fold transitive. These new examples also illustrate that an E0-semigroup of type Ilk need not be a tensor product of an E0-semigroup of type 110 and another of type I_k.