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Record W2244023066 · doi:10.46298/dmtcs.2839

Crystals from categorified quantum groups

2010· article· fr· W2244023066 on OpenAlex

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

VenueDiscrete Mathematics & Theoretical Computer Science · 2010
Typearticle
Languagefr
FieldMathematics
TopicAlgebraic structures and combinatorial models
Canadian institutionsUniversity of British Columbia
FundersNational Science Foundation
KeywordsMathematicsQuotientGrothendieck groupQuantumPure mathematicsQuantum groupAlgebra over a fieldHumanitiesPhysicsPhilosophyQuantum mechanics

Abstract

fetched live from OpenAlex

We study the crystal structure on categories of graded modules over algebras which categorify the negative half of the quantum Kac-Moody algebra associated to a symmetrizable Cartan data. We identify this crystal with Kashiwara's crystal for the corresponding negative half of the quantum Kac-Moody algebra. As a consequence, we show the simple graded modules for certain cyclotomic quotients carry the structure of highest weight crystals, and hence compute the rank of the corresponding Grothendieck group. Nous étudions la structure cristalline sur les catégories de modules gradués sur algèbres qui catégorifient la moitié négative du quantum de Kac-Moody algèbre associée à un ensemble de données symétrisables Cartan. Nous identifions ce cristal avec des cristaux de Kashiwara pour le négatif correspondant la moitié de l'algèbre de Kac-Moody quantum. En conséquence, nous montrons que les simples modules classés pour certains quotients cyclotomiques portent la structure des cristaux de poids le plus élevé, et donc calculons le rang du groupe correspondant Grothendieck.

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)0.002
metaresearch head score (Gemma)0.001
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow), Science and technology studies, Scholarly communication, Insufficient payload (model declined to judge)
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 score0.391
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0020.001
Meta-epidemiology (narrow)0.0010.001
Meta-epidemiology (broad)0.0010.000
Bibliometrics0.0000.001
Science and technology studies0.0010.009
Scholarly communication0.0010.001
Open science0.0030.002
Research integrity0.0010.002
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 head0.015
GPT teacher head0.268
Teacher spread0.252 · 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