Pith. sign in

REVIEW 1 cited by

The number of complete exceptional sequences for a Dynkin algebra

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 1307.7573 v3 pith:2IMVFIEF submitted 2013-07-29 math.RT math.CO

Mustafa A. A. Obaid , S. Khalid Nauman , Wafa S. Al Shammakh , Wafaa M. Fakieh , Claus Michael Ringel This is my paper · ORCID
classification math.RTmath.CO
keywords dynkinalgebracompleteexceptionalmodulessequencesalgebrasindecomposable
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original abstract

We consider Dynkin algebras, these are the hereditary artin algebras of finite representation type. The indecomposable modules for a Dynkin algebra correspond bijectively to the positive roots of a Dynkin diagram. Given a Dynkin algebra with n simple modules, a complete exceptional sequence is a sequence M_1,..., M_n of indecomposable modules such that Hom(M_i,M_j) = 0 = Ext(M_i,M_j) for i > j. The aim of this paper is to determine the number of complete exceptional sequences for any Dynkin algebra. There are direct connections between the representation theory of a Dynkin algebra A and the lattice L of non-crossing partitions of the same Dynkin type: As Ingalls and Thomas have shown, the lattice of the thick subcategories of mod A can be identified with L. Hubery and Krause have pointed out that this identification provides a bijection between the complete exceptional sequences for A and the maximal chains in L. Thus, our calculations may also be considered as a categorification of results concerning non-crossing partitions.

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. Enumerating iterated tilted algebras in type $A$

    math.RT 2026-08 conditional novelty 8.0 of 10

    Isoclasses of iterated tilted algebras of type A_n are in bijection with non-crossing spanning trees of a convex (n+1)-gon up to rotation, giving an explicit count.

Pith tools