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Record W3101421872

2 EQUIVARIANT MAP SUPERALGEBRAS

2016· article· en· W3101421872 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

Venuenot available
Typearticle
Languageen
FieldMathematics
TopicAlgebraic structures and combinatorial models
Canadian institutionsUniversity of Ottawa
Fundersnot available
KeywordsMathematicsEquivariant mapLie superalgebraPure mathematicsParameterized complexityTensor (intrinsic definition)Tensor productType (biology)SuperalgebraAbelian groupAlgebra over a fieldCombinatoricsAffine Lie algebraCurrent algebra
DOInot available

Abstract

fetched live from OpenAlex

Suppose a group $$\Gamma $$ acts on a scheme $$X$$ and a Lie superalgebra $$\mathfrak {g}$$ . The corresponding equivariant map superalgebra is the Lie superalgebra of equivariant regular maps from $$X$$ to $$\mathfrak {g}$$ . We classify the irreducible finite dimensional modules for these superalgebras under the assumptions that the coordinate ring of $$X$$ is finitely generated, $$\Gamma $$ is finite abelian and acts freely on the rational points of $$X$$ , and $$\mathfrak {g}$$ is a basic classical Lie superalgebra (or $$\mathfrak {sl}\,(n,n)$$ , $$n \ge 1$$ , if $$\Gamma $$ is trivial). We show that they are all (tensor products of) generalized evaluation modules and are parameterized by a certain set of equivariant finitely supported maps defined on $$X$$ . Furthermore, in the case that the even part of $$\mathfrak {g}$$ is semisimple, we show that all such modules are in fact (tensor products of) evaluation modules. On the other hand, if the even part of $$\mathfrak {g}$$ is not semisimple (more generally, if $$\mathfrak {g}$$ is of type I), we introduce a natural generalization of Kac modules and show that all irreducible finite dimensional modules are quotients of these. As a special case, our results give the first classification of the irreducible finite dimensional modules for twisted loop superalgebras.

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)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesInsufficient 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: Empirical
Teacher disagreement score0.069
Threshold uncertainty score0.997

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
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)0.0040.000

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 head0.041
GPT teacher head0.295
Teacher spread0.254 · 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