KMS states and topological *-algebras

SERGIO IGURI

Caracas, Venezuela

Workshop; Encuentro de Física-Matemática Caracas 2006; 2006

In the talk I'll present some results on thermal equilibrium states or KMS states and topological *-algebras. First I'll prove that the isomorphism between the space of states over a unital C*-algebra A and the set Cycl(A) of cyclic *-representations of A on Hilbert spaces, isomorphism stated by the classical GNS theorem, can be generalized for barrelled quasi-complete locally convex *-algebras. After an appropriate restatement of the GNS construction in terms of continuous positive forms instead of states, I´ll show that this isomorphism can be extended to an isomorphism between the family Hilb_A(A') of Hilbert subspaces of A' that are *-invariant under the dual action of A and the corresponding set of reproducing kernels. These multiple isomorphisms are not only topological ones but also isomorphisms for the strictly convex regular cone structure defined on Hilb_A(A'). At the end of the talk I'll discuss how these results can be used to describe KMS states on topological *-algebras.