Stephen Berman (University of Saskatchewan),
Bibliographic record
Abstract
Extended affine Lie algebras, or EALA’s for short, were introduced by Hoegh-Krohn and Torresani in 1990 [9] as natural generalizations of finite dimensional simple Lie algebras and affine Kac-Moody Lie algebras. Many of the basic facts about these algebras were proved in [1]. By definition EALA’s are complex Lie algebras that possess Cartan subalgebras and invariant forms, and hence they possess root systems which turn out to be extended affine root systems. Roots of length 0 are called isotropic roots, and they generate a lattice whose rank is referred to as the nullity of the EALA. As has been shown in [3], EALA’s of nullity 0 and 1 precisely coincide with finite dimensional simple algebras and affine Kac-Moody algebras respectively. Therefore there has been a lot of interest and activity in the last decade on the study of EALA’s of higher rank. An EALA L possesses an ideal Lc, called the core of L, which is defined to be the subalgebra of L generated by the root spaces of L corresponding to nonisotropic roots. (Lc is the derived algebra of L in nullity 0 and 1.) The quotient algebra Lcc: = Lc=Z(Lc), is called the centreless core of L. Y. Yoshii [14] has recently given an internal characterization of the Lie algebras, called centreless Lie tori, that arise as the centreless core of an EALA. Furthermore, the structure of an EALA is to a large extent governed by the structure of its centreless core. In fact, E. Neher [11] has recently announced a procedure that, given a
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot 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.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
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.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".