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Derivations commuting with abelian gauge actions on lattice systems
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Derivations commuting with abelian gauge actions on lattice systems

Ola Bratteli and Palle E. T Jørgensen
Communications in mathematical physics, Vol.87(no. 3), pp.353-364
1982
DOI: 10.1007/BF01206028

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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.
46L40 81E25

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