Mathematics – Operator Algebras
Scientific paper
2012-02-21
Mathematics
Operator Algebras
Changes to Definition 4.4. New Remark 4.5. Minor corrections
Scientific paper
We investigate existence of KMS states of Fowler's Nica-Toeplitz algebra $\mathcal{NT}(X)$ associated to a compactly aligned product system $X$ over a semigroup $P$ of Hilbert bimodules in terms of restrictions to the core algebra which satisfy appropriate scaling conditions. 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 many KMS$_\beta$ states of $\mathcal{NT}(X)$ associated to a scalar dynamics. Our results were motivated by, and generalize results of Laca and Raeburn obtained for the Toeplitz algebra of the affine semigroup over the natural numbers.
Hong Jeong Hee
Larsen Nadia S.
Szymanski Wojciech
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