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Record W7140790625 · doi:10.5802/jolt.843

On Chevalley's Formula for Structure Constants

2015· article· en· W7140790625 on OpenAlex
B. Casselman

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.

Bibliographic record

VenueJournal of Lie theory · 2015
Typearticle
Languageen
FieldMathematics
TopicMathematics and Applications
Canadian institutionsUniversity of British Columbia
Fundersnot available
KeywordsStructure constantsAlgebraic structureAlgebraic numberStructured program theoremPoint (geometry)Lie algebra

Abstract

fetched live from OpenAlex

In 1955, Chevalley proved the then surprising theorem that split semi-simple algebraic groups could be associated to every root system and defined over any ground field.The basic point in the construction was that complex semi-simple Lie algebras could be assigned an essentially unique Z -structure, in which the formulas for structure constants were particularly simple.His proof, which is that usually followed in the literature, does not appear transparent.In this paper, I'll show how an idea implicitly due to Jacques Tits leads to a more natural derivation.It remains valid for Kac-Moody algebras.

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 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: Empirical
Teacher disagreement score0.144
Threshold uncertainty score0.240

Codex and Gemma teacher scores by category

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

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 head0.119
GPT teacher head0.386
Teacher spread0.267 · 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