KMS states of quasi-free dynamics on Pimsner algebras

By Marcelo Laca, Sergey Neshveyev. 2003

105 citations recorded by the source corpus.

Abstract 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.

Subfields: Algebra and Number Theory, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/47982bde373707da57ff4d8f8db06c0e561e3dd3

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In Algebra and Number Theory

1. Aidan Sims
2. A. Rennie
3. Fedor Sukochev
4. Alan L. Carey
5. Iain Raeburn
6. Toke Meier Carlsen
7. Astrid an Huef
8. V. Gayral

In Mathematical Physics

1. Aidan Sims
2. A. Rennie
3. Alan L. Carey
4. Fedor Sukochev
5. Iain Raeburn
6. Toke Meier Carlsen
7. Astrid an Huef
8. V. Gayral

In Statistical and Nonlinear Physics

1. Aidan Sims
2. Alan L. Carey
3. Fedor Sukochev
4. V. Gayral
5. Astrid an Huef
6. Iain Raeburn
7. A. Rennie
8. Toke Meier Carlsen

Citations in the corpus

• Partial actions and KMS states on relative graph C⁎-algebras☆ (2013, background): “Introduction Characterizations of KMSβ states and ground states on C ∗-algebras of Toeplitz and CuntzKrieger type associated to a directed graph E have been obtained in different contexts by many authors, see for example [6], [7], [8], [10], [18], [24] and [26].”
• KMS states on the C∗-algebras of finite graphs (2012, methodology): “ying set C(En). The dynamics on T (X) is implemented by the unitaries Un t on X ⊗n= C(En) such that Un tδµ = e itnδ µ, and hence the operator Γ(e−βD) on the Fock module F(X) = L n≥0X ⊗n considered in [11] is multiplication by e−βn on X⊗n. A function ǫ∈ Σβ gives a trace τǫ : f → P v∈E0 f(v)ǫv on C(E ”
• Index Theory for Locally Compact Noncommutative Geometries (2011, background): “The discussion referred to in [38] is in the context of KMS weights, but by specialising to the case of invariant traces, the particular case of β-KMS weights with β = 0, we obtain the description we want.”