Journal article
Derivations commuting with abelian gauge actions on lattice systems
Communications in mathematical physics, Vol.87(no. 3), pp.353-364
1982
DOI: 10.1007/BF01206028
Abstract
Let τ be an action of a compact abelian group G on a C*-algebra A, and assume that the fixed-point subalgebra Aτ is an AF-algebra. We show that if δ is a closed *-derivation on A commuting with τ, and the restriction of δ to Aτ generates a one-parameter group of *-automorphisms, then δ itself is a generator. In particular, the result applies if τ is an infinite product action of G on a UHF algebra. Furthermore, if in this situation δ1 and δ2 are two derivations both satisfying the hypotheses on δ, and δ1 and δ2 have the same restriction to Aτ, then there exists a one-parameter subgroup of the action τ with generator δ0 such that D(δ1)∩D(δ2)∩D(δ0) is a joint core for the three derivations, and δ2=δ1+δ0 on this core. © 1982 Springer-Verlag.
Details
- Title: Subtitle
- Derivations commuting with abelian gauge actions on lattice systems
- Creators
- Ola Bratteli - University of WarwickPalle E. T Jørgensen
- Resource Type
- Journal article
- Publication Details
- Communications in mathematical physics, Vol.87(no. 3), pp.353-364
- DOI
- 10.1007/BF01206028
- ISSN
- 0010-3616
- eISSN
- 1432-0916
- Publisher
- Springer-Verlag
- Date published
- 1982
- Academic Unit
- Mathematics
- Record Identifier
- 9984241042802771
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