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Record W2062010666 · doi:10.1142/s0219199706002064

WEYL TYPE ALGEBRAS FROM QUANTUM TORI

2006· article· en· W2062010666 on OpenAlex

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

Bibliographic record

VenueCommunications in Contemporary Mathematics · 2006
Typearticle
Languageen
FieldMathematics
TopicAdvanced Topics in Algebra
Canadian institutionsWilfrid Laurier University
FundersNatural Sciences and Engineering Research Council of Canada
KeywordsMathematicsLie algebraAssociative algebraDifferential operatorCohomologyDimension (graph theory)Universal enveloping algebraType (biology)Pure mathematicsAlgebra over a fieldAlgebra representationCellular algebraCombinatorics

Abstract

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We introduce and study the quantum version of the differential operator algebra on Laurent polynomials and its associated Lie algebra over a field F of characteristic 0. The q-quantum torus F q is the unital associative algebra over F generated by [Formula: see text] subject to the defining relations t i t j = q i,j t j t i , where q i,i = 1, [Formula: see text]. Let D be a subspace of [Formula: see text] where ∂ i is the derivation on F q sending [Formula: see text] to [Formula: see text]. Then, the quantum differential operator algebra is the associative algebra F q [D]. Assume that F q [D] is simple as an associative algebra. We compute explicitly all 2-cocycles of F q [D], viewed as a Lie algebra. More precisely, we show that the second cohomology group of F q [D] has dimension n if D = 0, dimension 1 if dim D = 1, and dimension 0 if dim D > 1. We also determine all isomorphisms and anti-isomorphisms F q [D] → F q′ [D′] of simple associative algebras, and all isomorphisms F q [D]/F → F q′ [D′]/F of simple Lie 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 categoriesMeta-epidemiology (narrow)
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 score0.257
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 communication0.0000.000
Open science0.0020.001
Research integrity0.0000.001
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 head0.195
GPT teacher head0.386
Teacher spread0.191 · 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