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Record W2890693951 · doi:10.1016/j.jfa.2023.110228

Exotic C⁎-algebras of geometric groups

2023· article· en· W2890693951 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.
fundA Canadian funder is recorded on the work.

Bibliographic record

VenueJournal of Functional Analysis · 2023
Typearticle
Languageen
FieldMathematics
TopicAdvanced Operator Algebra Research
Canadian institutionsUniversity of WinnipegUniversity of Saskatchewan
FundersNatural Sciences and Engineering Research Council of Canada
KeywordsMathematicsNoncommutative geometryConjectureUnitary stateConnection (principal bundle)Group (periodic table)Pure mathematicsClass (philosophy)Locally compact groupLocally compact spaceUnitary representationPairwise comparisonCombinatoricsLie groupLawQuantum mechanics

Abstract

fetched live from OpenAlex

We consider a new class of potentially exotic group C*-algebras C ⁎ ( PF p ⁎ ( G ) ) for a locally compact group G , and its connection with the class of potentially exotic group C*-algebras C L p ⁎ ( G ) introduced by Brown and Guentner. Surprisingly, these two classes of C*-algebras are intimately related. By exploiting this connection, we show C L p ⁎ ( G ) = C ⁎ ( PF p ⁎ ( G ) ) for p ∈ ( 2 , ∞ ) , and the C*-algebras C L p ⁎ ( G ) are pairwise distinct for p ∈ ( 2 , ∞ ) when G belongs to a large class of nonamenable groups possessing the Haagerup property and either the rapid decay property or Kunze-Stein phenomenon by characterizing the positive definite functions that extend to positive linear functionals of C L p ⁎ ( G ) and C ⁎ ( PF p ⁎ ( G ) ) . This greatly generalizes earlier results of Okayasu (see [30] ) and the second author (see [40] ) on the pairwise distinctness of C L p ⁎ ( G ) for 2 < p < ∞ when G is either a noncommutative free group or the group SL ( 2 , R ) , respectively. As a byproduct of our techniques, we present two applications to the theory of unitary representations of a locally compact group G . Firstly, we give a short proof of the well-known Cowling-Haagerup-Howe Theorem, which presents sufficient condition implying the weak containment of a cyclic unitary representation of G in the left regular representation of G (see [14] ). Also we give a near solution to a 1978 conjecture of Cowling stated in [10] . This conjecture of Cowling states if G is a Kunze-Stein group and π is a unitary representation of G with cyclic vector ξ such that the map G ∋ s ↦ 〈 π ( s ) ξ , ξ 〉 belongs to L p ( G ) for some 2 < p < ∞ , then A π ⊆ L p ( G ) . We show B π ⊆ L p + ϵ ( G ) for every ϵ > 0 (recall A π ⊆ B π ).

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)0.002
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: Observational · Consensus signal: Observational
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.256
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.002
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0010.001
Bibliometrics0.0040.011
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 head0.109
GPT teacher head0.346
Teacher spread0.237 · 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