Pith. sign in

REVIEW 1 cited by

Brauer pairs for splendid Rickard equivalences

Not yet reviewed by Pith; the record is open.

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 2312.10258 v2 pith:SA5GG3RQ submitted 2023-12-15 math.RT math.GR

classification math.RTmath.GR
keywords brauerequivalencesrickardsplendidpairspermutationalgebrasblock
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

We define the notion of a Brauer pair of a chain complex, extending the notion of a Brauer pair of a $p$-permutation module introduced by Boltje and Perepelitsky. In fact, the Brauer pairs of a splendid Rickard equivalence $C$ coincide with the set of Brauer pairs of the corresponding $p$-permutation equivalence $\Lambda(C)$ induced by $C$. As a result, we derive structural results for splendid Rickard equivalences that correspond to known structural properties for $p$-permutation equivalences. In particular, we show splendid Rickard equivalences induce local splendid Rickard equivalences between normalizer block algebras as well as centralizer block algebras.

Discussion (0). Continue with ORCID 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. Permutation twisted cohomology, remixed

    math.RT 2025-08 conditional novelty 6.0 of 10

    For every finite p-group, the remixed twisted cohomology ring gives an injective comparison map from the Balmer spectrum of permutation modules, an open immersion when the ring is Noetherian.

Pith tools