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Record W7140557015 · doi:10.5802/jolt.472

Lie Group Invariants of Inhomogeneous Polynomial Vector Spaces

2007· article· en· W7140557015 on OpenAlex
J. T. Horwood

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.

fundA Canadian funder is recorded on the work.
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

VenueJournal of Lie theory · 2007
Typearticle
Languageen
FieldMathematics
TopicHolomorphic and Operator Theory
Canadian institutionsnot available
FundersCorpus Christi College, University of CambridgeUniversity of WaterlooNatural Sciences and Engineering Research Council of CanadaCambridge Commonwealth TrustDalhousie University
KeywordsLie groupPolynomialVector spaceLie algebraGeneral linear groupVector fieldAdjoint representationAlgebra over a field

Abstract

fetched live from OpenAlex

We present a method which efficiently generates Lie group invariants in the classical invariant theory of polynomials and its extensions to vector spaces of inhomogeneous polynomials under the actions of the general affine group and pseudo-Euclidean subgroups.Our derivation of the invariants uses the classical Cartan method of moving frames and requires no assumption on the degree of the polynomial or the number of variables.Consequently, we are able to express the invariants in a compact indicial notation.We employ our results to solve the equivalence and canonical forms problems for the vector space of inhomogeneous cubic polynomials in two real variables under the action of the Euclidean group.We show that the space partitions into twelve distinct classes of canonical forms, each admitting a system of invariants which globally separates its associated orbits.

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)0.005
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 score0.012
Threshold uncertainty score0.641

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0050.001
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0010.000
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)0.0010.000

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 head0.030
GPT teacher head0.297
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