KMS states of quasi-free dynamics on Pimsner algebras

A continuous one-parameter group of unitary isometries of a right-Hilbert C∗-bimodule induces a quasi-free dynamics on the Cuntz–Pimsner C∗-algebra of the bimodule and on its Toeplitz extension. The restriction of such a dynamics to the algebra of coefficients of the bimodule is trivial, and the corresponding KMS states of the Toeplitz–Cuntz–Pimsner and Cuntz–Pimsner C∗-algebras are characterized in terms of traces on the algebra of coefficients. This generalizes and sheds light onto various earlier results about KMS states of the gauge actions on Cuntz algebras, Cuntz–Krieger algebras, and crossed products by endomorphisms. We also obtain a more general characterization, in terms of KMS weights, for the case in which the inducing isometries are not unitary, and accordingly, the restriction of the quasi-free dynamics to the algebra of coefficients is nontrivial.