Homotopy of unitaries in simple<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msup><mml:mi>C</mml:mi><mml:mo>∗</mml:mo></mml:msup></mml:math>-algebras with tracial rank one

Lin, Huaxin

doi:10.1016/j.jfa.2009.11.020

Cited by 25 publications

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References 24 publications

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“…There is an extensive mathematical literature on the subject, see, e.g., Ref. [33]. Finally, we would like to mention that there is a somewhat related research direction in the context of AdS/CFT correspondence, which deals with the so-called long-range deformed spin chains [34,35] and T T deformations [36,37].…”

Section: Introductionmentioning

confidence: 99%

Quasiconserved quantities in the perturbed spin- 12 XXX model

2022

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We consider the isotropic spin-1 2 Heisenberg spin chain weakly perturbed by a local translationally and SU(2)-invariant perturbation. Starting from the local integrals of motion of the unperturbed model, we modify them in order to obtain quasiconserved integrals of motion (charges) for the perturbed model. Such quasiconserved quantities are believed to be responsible for the existence of the prethermalization phase at intermediate timescales. We find that for a sufficiently local perturbation the quasiconserved quantities indeed exist, and we construct an explicit form for the first few of them.

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Section: Introductionmentioning

confidence: 99%

Quasiconserved quantities in the perturbed spin- 12 XXX model

2022

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Kishimoto’s Conjugacy Theorems in Simple C*-Algebras of Tracial Rank One

Lin

2014

Integr. Equ. Oper. Theory

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Let A be a unital separable simple amenable C * -algebra with finite tracial rank which satisfies the Universal Coefficient Theorem (UCT). Suppose α and β are two automorphisms with the Rokhlin property that induce the same action on the K-theoretical data of A. We show that α and β are strongly outer conjugate and uniformly approximately conjugate, that is, there exists a sequence of unitaries {u n } ⊂ A and a sequence of strongly asymptotically inner automorphisms σ n such that α = Ad u n • σ n • β • σ −1 n and lim n→∞ u n − 1 = 0, and that the converse holds. We then give a K-theoretic description as to exactly when α and β are outer conjugate, at least under a mild restriction. Moreover, we show that given any K-theoretical data, there exists an automorphism α with the Rokhlin property which has the same K-theoretical data.

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Asymptotic unitary equivalence and classification of simple amenable C ∗-algebras

Lin

2010

Invent. math.

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208

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Let C and A be two unital separable amenable simple C * -algebras with tracial rank no more than one. Suppose that C satisfies the Universal Coefficient Theorem and suppose that ϕ 1 , ϕ 2 : C → A are two unital monomorphisms. We show that there is a continuous path ofT and a rotation related map R ϕ1,ϕ2 associated with ϕ 1 and ϕ 2 is zero.Applying this result together with a result of W. Winter, we give a classification theorem for a class A of unital separable simple amenable C * -algebras which is strictly larger than the class of separable C * -algebras whose tracial rank are zero or one. Tensor products of two C * -algebras in A are again in A. Moreover, this class is closed under inductive limits and contains all unital simple ASH-algebras whose state spaces of K 0 is the same as the tracial state spaces as well as some unital simple ASH-algebras whose K 0 -group is Z and tracial state spaces are any metrizable Choquet simplex. One consequence of the main result is that all unital simple AH-algebras which are Z-stable are isomorphic to ones with no dimension growth.

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Homotopy of unitaries in simpleC∗-algebras with tracial rank one

Cited by 25 publications

References 24 publications

Quasiconserved quantities in the perturbed spin- 12 XXX model

Quasiconserved quantities in the perturbed spin- 12 XXX model

Kishimoto’s Conjugacy Theorems in Simple C*-Algebras of Tracial Rank One

Asymptotic unitary equivalence and classification of simple amenable C ∗-algebras

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