Pith. sign in

REVIEW 1 cited by

Local structure of tame symmetric algebras of period four

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 2411.01235 v1 pith:3UBBVR3U submitted 2024-11-02 math.RT

classification math.RT
keywords algebrasgabrielquiversstructurefourlocalperiodsymmetric
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

In this paper we study the structure of Gabriel quivers of tame symmetric algebras of period four. More precisely, we focus on algebras having Gabriel quiver {\it biregular}, i.e. the numbers of arrows starting and ending at any vertex are equal, and do not exceed $2$. We describe the local structure of biregular Gabriel quivers of tame symmetric algebras of period four, including certain idempotent algebras. The main result of this paper shows that, in fact, these Gabriel quivers have local structure exactly as Gabriel quivers of so called {\it weighted surface algebras}, which partially extends known characterization of algebras of generalized quaternion type.

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. Periodicity shadows I: A new approach to combinatorics of periodic algebras

    math.RT 2024-11 conditional novelty 7.0 of 10

    Every Gabriel quiver of an algebra of generalized quaternion type reduces to a finite tame periodicity shadow, with all 2-cycles confined to a small list of local blocks.

Pith tools