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Categorical Landstad duality for actions

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S. Kaliszewski, John Quigg

Operator Algebras · Submitted 26 Dec 2006

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

The authors' main claim We show that the category A(G) of actions of a locally compact group G on C*-algebras (with equivariant nondegenerate *-homomorphisms into multiplier algebras) is equivalent, via a full-crossed-product functor, to a comma category of maximal coactions of G under the comultiplication (C*(G),delta_G); and also that A(G) is equivalent, via a reduced-crossed-product functor, to a comma category of normal coactions under the comultiplication.

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arXiv IDmath/0612771 (version 2)
Pith IDSMUOZUXD, Pith's permanent record of this paper and its review
CitationJohn Quigg, S. Kaliszewski. "Categorical Landstad duality for actions." arXiv:math/0612771 (2006). https://pith.science/paper/SMUOZUXD
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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, 2,518 input tokens.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.08 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.02 · compares with prior results 0.81 · mentions code or data availability 0.01.

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

We show that the category A(G) of actions of a locally compact group G on C*-algebras (with equivariant nondegenerate *-homomorphisms into multiplier algebras) is equivalent, via a full-crossed-product functor, to a comma category of maximal coactions of G under the comultiplication (C*(G),delta_G); and also that A(G) is equivalent, via a reduced-crossed-product functor, to a comma category of normal coactions under the comultiplication. This extends classical Landstad duality to a category equivalence, and allows us to identify those C*-algebras which are isomorphic to crossed products by G as precisely those which form part of an object in the appropriate comma category.

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 show that the category A(G) of actions of a locally compact group G on C*-algebras (with equivariant nondegenerate *-homomorphisms into multiplier algebras) is equivalent, via a full-crossed-product functor, to a comma category of maximal coactions of G under the comultiplication (C*(G),delta_G); and also that A(G) is equivalent, via a reduced-crossed-product functor, to a comma category of normal coactions under the comultiplication. result 0.81 0.96 0.85 asserted 1.00
s1 This extends classical Landstad duality to a category equivalence, and allows us to identify those C*-algebras which are isomorphic to crossed products by G as precisely those which form part of an object in the appropriate comma category. interpretation 0.95 0.89 0.39 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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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 show that the category A(G) of actions of a locally compact group G on C*-algebras (with equivariant nondegenerate *-homomorphisms into multiplier algebras) is equivalent, via a full-crossed-product functor, to a comma category of maximal coactions of G under the comultiplication (C*(G),delta_G); and also that A(G) is equivalent, via a reduced-crossed-product functor, to a comma category of normal coactions under the comultiplication. This extends classical Landstad duality to a category equivalence, and allows us to identify those C*-algebras which are isomorphic to crossed products by G as precisely those which form part of an object in the appropriate comma category.

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