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Record W3022426023 · doi:10.48550/arxiv.2005.04471

$C^*$-Envelope and Dilation Theory of Semigroup Dynamical Systems

2020· preprint· en· W3022426023 on OpenAlexaff
Boyu Li

Bibliographic record

VenuearXiv (Cornell University) · 2020
Typepreprint
Languageen
FieldMathematics
TopicAdvanced Operator Algebra Research
Canadian institutionsUniversity of Victoria
Fundersnot available
KeywordsMathematicsSemigroupCommutative propertyOperator algebraPure mathematicsOperator (biology)Self-adjoint operatorEnvelope (radar)Dilation (metric space)Dynamical systems theoryAlgebra over a fieldDiscrete mathematicsHilbert spaceCombinatoricsPhysicsComputer scienceQuantum mechanics

Abstract

fetched live from OpenAlex

In this paper, we construct, for a certain class of semigroup dynamical systems, two operator algebras that are universal with respect to their corresponding covariance conditions: one being self-adjoint, and another being non-self-adjoint. We prove that the $C^*$-envelope of the non-self-adjoint operator algebra is precisely the self-adjoint one. This result leads to a number of new examples of operator algebras and their $C^*$-envelopes, with many from number fields and commutative rings. We further establish the functoriality of these operator algebras along with their applications.

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)0.001
metaresearch head score (Gemma)0.002
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 score0.003
Threshold uncertainty score0.009

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0010.002
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.001
Bibliometrics0.0000.000
Science and technology studies0.0010.002
Scholarly communication0.0020.003
Open science0.0000.001
Research integrity0.0010.001
Insufficient payload (model declined to judge)0.0030.000

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 head0.146
GPT teacher head0.247
Teacher spread0.101 · 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".

Quick stats

Citations1
Published2020
Admission routes1
Has abstractyes

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