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- W3009955418 abstract "Given a quasi-lattice ordered group $(G,P)$ and a compactly aligned product system $X$ of essential C$^*$-correspondences over the monoid $P$, we show that there is a bijection between the gauge-invariant KMS$_beta$-states on the Nica-Toeplitz algebra $mathcal{NT}(X)$ of $X$ with respect to a gauge-type dynamics, on one side, and the tracial states on the coefficient algebra $A$ satisfying a system (in general infinite) of inequalities, on the other. This strengthens and generalizes a number of results in the literature in several directions: we do not make any extra assumptions on $P$ and $X$, and our result can, in principle, be used to study KMS-states at any finite inverse temperature $beta$. Under fairly general additional assumptions we show that there is a critical inverse temperature $beta_c$ such that for $beta>beta_c$ all KMS$_beta$-states are of Gibbs type, hence gauge-invariant, in which case we have a complete classification of KMS$_beta$-states in terms of tracial states on $A$, while at $beta=beta_c$ we have a phase transition manifesting itself in the appearance of KMS$_beta$-states that are not of Gibbs type. In the case of right-angled Artin monoids we show also that our system of inequalities for traces on $A$ can be reduced to a much smaller system, a finite one when the monoid is finitely generated. Most of our results generalize to arbitrary quasi-free dynamics on $mathcal{NT}(X)$." @default.
- W3009955418 created "2020-03-13" @default.
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- W3009955418 date "2020-03-03" @default.
- W3009955418 modified "2023-10-18" @default.
- W3009955418 title "KMS States on Nica-Toeplitz $$hbox {C}^*$$-algebras" @default.
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- W3009955418 doi "https://doi.org/10.1007/s00220-020-03711-6" @default.
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