KMS states on Nica-Toeplitz algebras of product systems

We investigate KMS states of Fowler’s Nica-Toeplitz algebra $\mathcal{N}\mathcal{T}(X)$ associated to a compactly aligned product system $X$ over a semigroup $P$ of Hilbert bimodules. This analysis relies on restrictions of these states to the core algebra which satisfy appropriate scaling conditions. The concept of product system of finite type is introduced. If $(G,P)$ is a lattice ordered group and $X$ is a product system of finite type over $P$ satisfying certain coherence properties, we construct KMS${}_{\beta }$ states of $\text{NT}(X)$ associated to a scalar dynamics from traces on the coefficient algebra of the product system. Our results were motivated by, and generalize some of the results of Laca and Raeburn obtained for the Toeplitz algebra of the affine semigroup over the natural numbers.