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Cup Products in Hopf-Cyclic Cohomology

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Masoud Khalkhali (Mathematics Department, University of Western Ontario, London ON, Canada), Bahram Rangipour (Mathematics, Statistics Department, Univerity of Victoria, Victoria BC

Quantum Algebra · Submitted 30 Oct 2004

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

The authors' main claim We construct cup products of two different kinds for Hopf-cyclic cohomology.

how it is stated · asserted 1.00 read the record →

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arXiv IDmath/0411003 (version 1)
CitationBahram Rangipour (Mathematics, Canada), London ON, Masoud Khalkhali (Mathematics Department, Statistics Department, Univerity of Victoria, University of Western Ontario, Victoria BC. "Cup Products in Hopf-Cyclic Cohomology." arXiv:math/0411003 (2004). https://pith.science/paper/math/0411003
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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, 2,879 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.14 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.94 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We construct cup products of two different kinds for Hopf-cyclic cohomology. When the Hopf algebra reduces to the ground field our first cup product reduces to Connes' cup product in ordinary cyclic cohomology. The second cup product generalizes Connes-Moscovici's characteristic map for actions of Hopf algebras on algebras.

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 construct cup products of two different kinds for Hopf-cyclic cohomology. contribution 1.00 0.96 0.68 asserted 1.00
s1 When the Hopf algebra reduces to the ground field our first cup product reduces to Connes' cup product in ordinary cyclic cohomology. result 0.63 0.73 0.12 asserted 1.00
s2 The second cup product generalizes Connes-Moscovici's characteristic map for actions of Hopf algebras on algebras. interpretation 0.38 0.67 0.20 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.79 · 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 construct cup products of two different kinds for Hopf-cyclic cohomology. When the Hopf algebra reduces to the ground field our first cup product reduces to Connes' cup product in ordinary cyclic cohomology. The second cup product generalizes Connes-Moscovici's characteristic map for actions of Hopf algebras on algebras.

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