Journal article
Decomposition of unbounded derivations into invariant and approximately inner parts
Journal für die reine und angewandte Mathematik, Vol.1984(346), pp.166-193
1984
DOI: 10.1515/crll.1984.346.166
Abstract
Let τ: G → Aut ǣ be a compact abelian ergodic action on a simple C*-algebra ǣ, and denote by ǣF the subalgebra of G-fmite elements. If δ: ǣF → ǣ is a *-derivation, then there exist a one-parameter subgroup t ↦ g(t) of G and an approximately inner derivation δ such that δ = δ0 + δ where δ0 is the generator of t ↦ τ(g(t)). This decomposition is unique. Suppose that Ĝ is finitely generated. If δ takes ǣF into ǣF, then δ is inner. Also, for almost all ergodic actions (ǣ, τ), if δ takes ǣF into the subalgebra ǣ∞ of infmitely differentiable elements then δ is inner. Note that when δ is inner, δ is the generator of a one-parameter group.
Details
- Title: Subtitle
- Decomposition of unbounded derivations into invariant and approximately inner parts
- Creators
- P. E. T JorgensenG. A ElliottO Bratteli
- Resource Type
- Journal article
- Publication Details
- Journal für die reine und angewandte Mathematik, Vol.1984(346), pp.166-193
- Publisher
- Walter de Gruyter, Berlin / New York
- DOI
- 10.1515/crll.1984.346.166
- ISSN
- 0075-4102
- eISSN
- 1435-5345
- Language
- German
- Date published
- 1984
- Academic Unit
- Mathematics
- Record Identifier
- 9984241058302771
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