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Record W3142703287 · doi:10.1007/s10468-022-10165-y

Superpotentials and Quiver Algebras for Semisimple Hopf Actions

2022· article· en· W3142703287 on OpenAlex
Simon Crawford

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

VenueAlgebras and Representation Theory · 2022
Typearticle
Languageen
FieldMathematics
TopicAlgebraic structures and combinatorial models
Canadian institutionsnot available
FundersUniversity of WaterlooCanadian Network for Research and Innovation in Machining Technology, Natural Sciences and Engineering Research Council of CanadaUniversity of ManchesterLondon Mathematical SocietyUniversity of Washington
KeywordsQuiverMathematicsSuperpotentialQuotientHopf algebraIsomorphism (crystallography)Pure mathematicsAlgebra over a fieldBiproductAction (physics)Cellular algebraAlgebra representationFunctorSupersymmetryMathematical physicsPhysics

Abstract

fetched live from OpenAlex

Abstract We consider the action of a semisimple Hopf algebra H on an m -Koszul Artin–Schelter regular algebra A . Such an algebra A is a derivation-quotient algebra for some twisted superpotential w , and we show that the homological determinant of the action of H on A can be easily calculated using w . Using this, we show that the smash product A # H is also a derivation-quotient algebra, and use this to explicitly determine a quiver algebra Λ to which A # H is Morita equivalent, generalising a result of Bocklandt–Schedler–Wemyss. We also show how Λ can be used to determine whether the Auslander map is an isomorphism. We compute a number of examples, and show how several results for the quantum Kleinian singularities studied by Chan–Kirkman–Walton–Zhang follow using our techniques.

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 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 score0.006
Threshold uncertainty score0.659

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 studies0.0010.000
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 head0.052
GPT teacher head0.335
Teacher spread0.283 · 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