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Groups andC*-Algebras from a 4-Dimensional Anzai Flow

2002· article· en· W2015136416 on OpenAlex
Paul Milnes

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.
fundA Canadian funder is recorded on the work.

Bibliographic record

VenueMathematische Nachrichten · 2002
Typearticle
Languageen
FieldMathematics
TopicAdvanced Operator Algebra Research
Canadian institutionsWestern University
FundersNatural Sciences and Engineering Research Council of Canada
KeywordsQuotientMathematicsAlgebra over a fieldFlow (mathematics)Group (periodic table)Simple (philosophy)CombinatoricsPure mathematicsPhilosophyGeometryPhysicsEpistemology

Abstract

fetched live from OpenAlex

The rotation flow on the circle T gives a concrete representation of the irrational rotation algebra, which is an in finite dimensional simple quotient of the group C*-algebra of the discrete Heisenberg group H3 analogously certain 2- and 3-dimensional Anzai flows on T2 and T3are known to give concrete representations of the corresponding quotients of the group C*-algebras of the groups H4 and H5,5. Considered here is the (minimal, effective) 4-dimensional Anzai flow F = (ℤ, T4) generated by the homeomorphism (y, x, w, v) ↦ (λy, yx, xw, wv); a group H6,10 is determined by F the faithful in finite dimensional simple quotients of whose group C*-algebra C*-(H6,10 have concrete representations given by F. Furthermore, the rest of the infinite dimensional simple quotients of C*-(H6,10 are identified and displayed as C*-crossed products generated by minimal effective actions and also as matrix algebras over simple C*-algebras from groups of lower dimension; these lower dimensional groups are H3 and subgroups of H4 and H5,5.

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.

Full frame distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.

metaresearch head score (Codex)0.001
metaresearch head score (Gemma)0.001
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow), Insufficient payload (model declined to judge)
Consensus categoriesInsufficient payload (model declined to judge)
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: none
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.656
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.001
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0010.000
Bibliometrics0.0000.001
Science and technology studies0.0000.000
Scholarly communication0.0000.001
Open science0.0010.000
Research integrity0.0000.001
Insufficient payload (model declined to judge)0.0100.003

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 head0.066
GPT teacher head0.308
Teacher spread0.242 · 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