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Record W2231662792 · doi:10.1090/tran/7045

Isomorphisms of tensor algebras arising from weighted partial systems

2016· preprint· en· W2231662792 on OpenAlexafffund
Adam Dor-On

Bibliographic record

VenueTransactions of the American Mathematical Society · 2016
Typepreprint
Languageen
FieldMathematics
TopicAdvanced Operator Algebra Research
Canadian institutionsUniversity of Waterloo
FundersOntario Trillium Foundation
KeywordsIsomorphism (crystallography)MathematicsTensor productTensor product of algebrasBounded functionTensor (intrinsic definition)Pure mathematicsAlgebraic numberAlgebraic structureSymmetric tensorAlgebra over a fieldTensor algebraTensor product of Hilbert spacesTensor contractionJordan algebraAlgebra representationExact solutions in general relativityMathematical analysis

Abstract

fetched live from OpenAlex

We continue the study of isomorphisms of tensor algebras associated to C ∗ C^* -correspondences in the sense of Muhly and Solel. Inspired by recent work of Davidson, Ramsey, and Shalit, we solve isomorphism problems for tensor algebras arising from weighted partial dynamical systems. We provide complete bounded / isometric classification results for tensor algebras arising from weighted partial systems, both in terms of the C ∗ C^* -correspondences associated to them and in terms of the original dynamics. We use this to show that the isometric isomorphism and algebraic / bounded isomorphism problems are two distinct problems that require separate criteria to be solved. Our methods yield alternative proofs to classification results for Peters’ semi-crossed product due to Davidson and Katsoulis and for multiplicity-free graph tensor algebras due to Katsoulis, Kribs, and Solel.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

How this classification was reachedexpand

Full frame machine prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.

metaresearch head score (Codex)0.002
metaresearch head score (Gemma)0.004
Version: metacan-v3-hybrid-931329e0061cValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: none
Teacher disagreement score0.008
Threshold uncertainty score0.027

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0020.004
Meta-epidemiology (narrow)0.0010.000
Meta-epidemiology (broad)0.0010.002
Bibliometrics0.0020.002
Science and technology studies0.0020.003
Scholarly communication0.0030.007
Open science0.0010.004
Research integrity0.0010.002
Insufficient payload (model declined to judge)0.0080.001

Machine scores (provisional)

The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.

Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.

Opus teacher head0.042
GPT teacher head0.329
Teacher spread0.287 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it

Classification

machine, unvalidated

Machine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.

The models applied no category: nothing in the taxonomy fit this work.
Study designTheoretical or conceptual
Domainnot available
GenreEmpirical

How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".

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Citations0
Published2016
Admission routes2
Has abstractyes

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Same venueTransactions of the American Mathematical SocietySame topicAdvanced Operator Algebra ResearchFrench-language works237,207