Gauge groups of \(E_{0}\)-semigroups obtained from powers weights (Q2905261)
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scientific article; zbMATH DE number 6072503
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Gauge groups of \(E_{0}\)-semigroups obtained from powers weights |
scientific article; zbMATH DE number 6072503 |
Statements
27 August 2012
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\(E_0\)-semigroup
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Arveson system
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Gauge groups of \(E_{0}\)-semigroups obtained from powers weights (English)
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\(E_0\)-semigroups (that is, semigroups of unital endomorphims) on \(B(H)\) are classified by their Arveson systems up to cocycle conjugacy. The gauge group of an \(E_0\)-semigroup is the automorphism group of its associated Arveson system and, therefore, a cocycle conjugacy invariant. Except for CCR-flows, the gauge group is usually quite difficult to compute. Based on Powers's technique to analyse spatial \(E_0\)-semigroups up to cocycle conjugacy in terms of CP-flows, the authors compute explicitly the gauge groups of several type II\(_0\) \(E_0\)-semigroups.
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