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Record W1581189410 · doi:10.4153/cmb-2003-056-1

Cartan Subalgebras of

2003· article· en· W1581189410 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.

venuePublished in a venue whose home country is Canada.
no affNo Canadian affiliation: this work is invisible to an affiliation-only frame.
No Canadian affiliation. An affiliation-only frame, the usual design, would never have seen this work. It is one of the works that make the case for inverting the frame.

Bibliographic record

VenueCanadian Mathematical Bulletin · 2003
Typearticle
Languageen
FieldMathematics
TopicAdvanced Topics in Algebra
Canadian institutionsnot available
FundersDeutsche ForschungsgemeinschaftNational Science Foundation
KeywordsCartan subalgebraMathematicsSubalgebraNilpotentCentralizer and normalizerLinear subspacePure mathematicsAlgebraically closed fieldLie algebraRank (graph theory)Adjoint representationCartan matrixSpace (punctuation)Field (mathematics)Vector spaceDiscrete mathematicsAlgebra over a fieldCombinatoricsFundamental representationUniversal enveloping algebraNon-associative algebraWeight

Abstract

fetched live from OpenAlex

Abstract Let V be a vector space over a field of characteristic zero and V * be a space of linear functionals on V which separate the points of V . We consider V ⊗ V * as a Lie algebra of finite rank operators on V , and set (V, V * ) := V ⊗ V * . We define a Cartan subalgebra of (V, V * ) as the centralizer of a maximal subalgebra every element of which is semisimple, and then give the following description of all Cartan subalgebras of (V;V * ) under the assumption that is algebraically closed. A subalgebra of (V, V * ) is a Cartan subalgebra if and only if it equals for some one-dimensional subspaces V j ⊆ V and (V j ) * ⊆ V * with (Vi) * (V j ) = δ ij and such that the spaces . We then discuss explicit constructions of subspaces V j and (V j ) * as above. Our second main result claims that a Cartan subalgebra of (V, V * ) can be described alternatively as a locally nilpotent self-normalizing subalgebra whose adjoint representation is locally finite, or as a subalgebra h which coincides with the maximal locally nilpotent h-submodule of (V, V * ), and such that the adjoint representation of is locally finite.

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)0.000
metaresearch head score (Gemma)0.005
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesInsufficient 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: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.448
Threshold uncertainty score0.998

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.005
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)0.0250.003

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 head0.030
GPT teacher head0.279
Teacher spread0.249 · 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