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C*-algebras of Hilbert module product systems

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Ilan Hirshberg

Operator Algebras · Submitted 23 May 2002

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

The authors' main claim By exhibiting a homotopy of quasihomomorphisms, we prove that those algebras are $K$-contractible.

how it is stated · asserted 1.00 read the record →

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arXiv IDmath/0205238 (version 2)
Pith IDLZJAN6NB, Pith's permanent record of this paper and its review
CitationIlan Hirshberg. "C*-algebras of Hilbert module product systems." arXiv:math/0205238 (2002). https://pith.science/paper/LZJAN6NB
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The compiled record

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, 3,800 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.07 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.09 · compares with prior results 0.90 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

We consider a class of C*-algebras associated to one parameter continuous tensor product systems of Hilbert modules, which can be viewed as continuous counterparts of Pimsner's Toeplitz algebras. By exhibiting a homotopy of quasihomomorphisms, we prove that those algebras are $K$-contractible. One special case is closely related to the Rieffel-Wiener-Hopf extension of a crossed product by R considered by Rieffel and by Pimsner and Voiculescu, and can be used to produce a new proof of Connes' analogue of the Thom isomorphism and in particular of Bott periodicity. Another special case is closely related to Arveson's spectral C*-algebras, and is used to settle Arveson's problem of computing their K-theory, extending earlier results of Zacharias to cover the general case.

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 We consider a class of C*-algebras associated to one parameter continuous tensor product systems of Hilbert modules, which can be viewed as continuous counterparts of Pimsner's Toeplitz algebras. contribution 0.89 0.60 0.05 asserted 0.97
s1 By exhibiting a homotopy of quasihomomorphisms, we prove that those algebras are $K$-contractible. result 0.95 0.96 0.77 asserted 1.00
s2 One special case is closely related to the Rieffel-Wiener-Hopf extension of a crossed product by R considered by Rieffel and by Pimsner and Voiculescu, and can be used to produce a new proof of Connes' analogue of the Thom isomorphism and in particular of Bott periodicity. interpretation 0.45 0.76 0.08 asserted 0.91
s3 Another special case is closely related to Arveson's spectral C*-algebras, and is used to settle Arveson's problem of computing their K-theory, extending earlier results of Zacharias to cover the general case. result 0.66 0.88 0.08 asserted 1.00

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

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  • C citations
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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

We consider a class of C*-algebras associated to one parameter continuous tensor product systems of Hilbert modules, which can be viewed as continuous counterparts of Pimsner's Toeplitz algebras. By exhibiting a homotopy of quasihomomorphisms, we prove that those algebras are $K$-contractible. One special case is closely related to the Rieffel-Wiener-Hopf extension of a crossed product by R considered by Rieffel and by Pimsner and Voiculescu, and can be used to produce a new proof of Connes' analogue of the Thom isomorphism and in particular of Bott periodicity. Another special case is closely related to Arveson's spectral C*-algebras, and is used to settle Arveson's problem of computing their K-theory, extending earlier results of Zacharias to cover the general case.

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