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Record W2012162267 · doi:10.4153/cmb-2003-049-7

Symmetries of Kirchberg Algebras

2003· article· en· W2012162267 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
Fundersnot available
KeywordsMathematicsAutomorphismUnitalCountable setEquivariant mapElement (criminal law)Order (exchange)Abelian groupDiscrete mathematicsPure mathematicsCombinatoricsAlgebra over a field

Abstract

fetched live from OpenAlex

Abstract Let G 0 and G 1 be countable abelian groups. Let γ i be an automorphism of G i of order two. Then there exists a unital Kirchberg algebra A satisfying the Universal Coefficient Theorem and with [1 A ] = 0 in K 0 (A), and an automorphism α ∈ Aut(A) of order two, such that K 0 (A) ≅ G 0 , such that K 1 (A) ≅ G 1 , and such that α * : K i (A) → K i (A) is γ i . As a consequence, we prove that every -graded countable module over the representation ring R( ) of is isomorphic to the equivariant K-theory K (A) for some action of on a unital Kirchberg algebra A . Along the way, we prove that every not necessarily finitely generated [ ]-module which is free as a -module has a direct sum decomposition with only three kinds of summands, namely [ ] itself and on which the nontrivial element of acts either trivially or by multiplication by −1.

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)0.011
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMetaresearch, Insufficient 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: none
Teacher disagreement score0.716
Threshold uncertainty score0.998

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.011
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)0.0220.003

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 head0.032
GPT teacher head0.280
Teacher spread0.248 · 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