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C*-crossed products and shift spaces

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Toke Meier Carlsen, Sergei Silvestrov

Operator Algebras · Submitted 21 Dec 2005

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We show that it has the C*-algebra defined in [Carlsen and Matsumoto: Some remarks on the C*-algebras associated with subshifts] as a quotient, and possesses properties indicating that it can be thought of as the universal C*-algebra associated to a shift space.

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arXiv IDmath/0512488 (version 1)
Pith IDOQSW2HH4, Pith's permanent record of this paper and its review
CitationSergei Silvestrov, Toke Meier Carlsen. "C*-crossed products and shift spaces." arXiv:math/0512488 (2005). https://pith.science/paper/OQSW2HH4
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,166 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.09 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.92 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

In this article, we use Exel's construction to associate a C*-algebra to every shift space. We show that it has the C*-algebra defined in [Carlsen and Matsumoto: Some remarks on the C*-algebras associated with subshifts] as a quotient, and possesses properties indicating that it can be thought of as the universal C*-algebra associated to a shift space. We also consider its representations, relationship to other C*-algebras associated to shift spaces, show that it can be viewed as a generalization of the universal Cuntz-Krieger algebra, discuss uniqueness and a faithful representation, provide conditions for it being nuclear, for satisfying the UCT, for being simple, and for being purely infinite, show that the constructed algebras and thus their K-theory, $K_0$ and $K_1$, are conjugacy invariants of one-sided shift spaces, present formulas for those invariants, and also present a description of the structure of gauge invariant ideals.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 In this article, we use Exel's construction to associate a C*-algebra to every shift space. contribution 0.88 0.96 0.14 asserted 1.00
s1 We show that it has the C*-algebra defined in [Carlsen and Matsumoto: Some remarks on the C*-algebras associated with subshifts] as a quotient, and possesses properties indicating that it can be thought of as the universal C*-algebra associated to a shift space. result 0.81 0.93 0.55 asserted 0.63
s2 We also consider its representations, relationship to other C*-algebras associated to shift spaces, show that it can be viewed as a generalization of the universal Cuntz-Krieger algebra, discuss uniqueness and a faithful representation, provide conditions for it being nuclear, for satisfying the UCT, for being simple, and for being purely infinite, show that the constructed algebras and thus their K-theory, $K_0$ and $K_1$, are conjugacy invariants of one-sided shift spaces, present formulas for those invariants, and also present a description of the structure of gauge invariant ideals. contribution 0.82 0.96 0.25 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.88 · evidence from proof or derivation 1.00.

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  • references and citing sentences
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  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

In this article, we use Exel's construction to associate a C*-algebra to every shift space. We show that it has the C*-algebra defined in [Carlsen and Matsumoto: Some remarks on the C*-algebras associated with subshifts] as a quotient, and possesses properties indicating that it can be thought of as the universal C*-algebra associated to a shift space. We also consider its representations, relationship to other C*-algebras associated to shift spaces, show that it can be viewed as a generalization of the universal Cuntz-Krieger algebra, discuss uniqueness and a faithful representation, provide conditions for it being nuclear, for satisfying the UCT, for being simple, and for being purely infinite, show that the constructed algebras and thus their K-theory, $K_0$ and $K_1$, are conjugacy invariants of one-sided shift spaces, present formulas for those invariants, and also present a description of the structure of gauge invariant ideals.

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