Pith. sign in

REVIEW 2 cited by

A Survey on Han's Conjecture

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2301.07511 v2 pith:FZBOXQQG submitted 2023-01-16 math.KT math.CTmath.RAmath.RT

Guilherme da Costa Cruz This is my paper · ORCID
classification math.KTmath.CTmath.RAmath.RT
keywords cohomologyconjecturedimensionglobalhochschildsurveyalgebraalgebras
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
read the original abstract

In 1989, D. Happel pointed out for a possible connection between the global dimension of a finite-dimensional algebra and its Hochschild cohomology: is it true that the vanishing of Hochschild cohomology higher groups is sufficient to deduce that the global dimension is finite? After the discovery of a counterexample, Y. Han proposed, in 2006, to reformulate this question to homology. In this survey, after introducing the concepts and results involved, I present the efforts made until now towards the comprehension of Han's conjecture; which includes: examples of algebras that have been proven to satisfy it and extensions that preserve it.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Protected corners and a trichotomy for Han's conjecture

    math.RT 2026-07 conditional novelty 7.0 of 10

    All three simples of a three-vertex Gap-A failure cannot all have infinite projective dimension; the two-infinite case is forced to be a 'mutual dumbbell', and a protected corner forces Ext^n(S_x,S_x) nonzero in every degree.

  2. Stability for socle-projective categories of type $\mathbb{A}$

    math.RT 2025-01 conditional novelty 6.0 of 10

    Every indecomposable peak P-space of a type A poset is stable under a bilinear-form weight and under an angle stability function from a new geometric model.

Pith tools