Representations of the O*-algebra Qi of observables corresponding to thermal equilibrium of a system at given temperature T and chemical potential μ are studied. Both for finite and for infinite systems it is shown that the representation is reducible and that there exists a conjugation in the representation space, which maps the von Neumann algebra spanned by the representative of 21 onto its commutant. This means that there is an equivalent anti-linear representation of £1 in the commutant. The relation of these properties with the Kubo-Martin-Schwinger boundary condition is discussed.

It is shown that K.M.S.-states are locally normal on a great number of C*-algebras that may be of interest in Quantum Statistical Mechanics. The lattice structure and the Choquet-simplex structure of various sets of states are investigated. In this respect special attention is payed to the interplay of the K.M.S.-automorphism group with other automorphism groups under whose action K.M.S.-states are possibly invariant. A seemingly weaker notion than G-abelianness of the algebra of observables, namely G'abelianness, is introduced and investigated. Finally a necessary and sufficient condition (on a C*-algebra with a sequential separable factor funnel) for decomposition of a locally normal state into locally normal states is given.

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