Pith. sign in

REVIEW 1 cited by

Delooping levels

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 2410.16422 v1 pith:ZPDFZHR7 submitted 2024-10-21 math.RT

Marcos Barrios , Marcelo Lanzilotta , Gustavo Mata This is my paper
classification math.RT
keywords delldeloopingdimensionalgebrafinitistichomologicalinvariantlevel
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

In [8] V. G\'elinas introduced a homological invariant, called {\it delooping level} (dell), that bounds the finitistic dimension. In this article, we introduce another homological invariant (Dell) related to the delooping level for an Artin algebra. We compare this new tool with other dimensions as the finitistic dimension or the $\phi$-dimension (where $\phi$ is the first Igusa-Todorov function), and we also generalize Theorem 4.3. from [9] to truncated path algebras (Theorem 4.18). Finally, we show that for a monomial algebra $A$ the difference dell($A$) - Findim($A$) can be arbitrarily large (Example 4.22).

Discussion (0). Sign in to comment.

Forward citations

Cited by 1 Pith paper

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

  1. Homological Invariants of Left and Right Serial Path Algebras

    math.RT 2025-06 conditional novelty 6.0 of 10

    In right serial path algebras the left delooping level equals the right finitistic dimension; left serial algebras need an extra condition, with a counterexample where the derived delooping level does better.

Pith tools