Journal article
Unbounded derivations tangential to compact groups of automorphisms
Journal of functional analysis, Vol.48(1), pp.107-133
1982
DOI: 10.1016/0022-1236(82)90064-7
Abstract
We consider unbounded derivations in C ∗ -algebras commuting with compact groups of ∗ -automorphisms. A closed ∗ -derivation δ in a C ∗ -algebra U is said to be a generator if there exists a strongly continuous one-parameter subgroup t ∈ R → τ ( t )⊂ Aut( U ) such that δ = d dt τ(t)¦ t = 0 . If δ is known to commute with a compact abelian action α : G →Aut( U ), and if δ ( a ) = 0 for all a in the fixed point algebra U α of the action G , then we show that δ is necessarily a generator. Moreover, in any faithful G -covariant representation, there is a commutative operator field γ ∈ Ĝ → v(γ) such that v(γ) ∗ = −v(γ), v(γ) is possibly unbounded but affiliated with the center of { U α }″, and e tδ ( x ) = xe tv ( γ ) for all x in the Arveson spectral subspace U α (γ). In particular, if U is the CAR algebra over an infinite-dimensional Hilbert space and α is the gauge group, then any such derivation δ is a scalar multiple of the generator of the gauge group.
Details
- Title: Subtitle
- Unbounded derivations tangential to compact groups of automorphisms
- Creators
- Ola BratteliPalle E.T Jørgensen
- Resource Type
- Journal article
- Publication Details
- Journal of functional analysis, Vol.48(1), pp.107-133
- DOI
- 10.1016/0022-1236(82)90064-7
- ISSN
- 1096-0783
- eISSN
- 1096-0783
- Language
- English
- Date published
- 1982
- Academic Unit
- Mathematics
- Record Identifier
- 9983985963102771
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